When Gov. Kathy Hochul first took office in 2021, she was a relative unknown. Few New Yorkers knew how to pronounce her name, let alone what Ms. Hochul, Andrew M. Cuomo’s seldom-seen lieutenant governor, stood for.

Since then, she has honed an executive style that is equal parts practical and protective. And while many elements inform her politics — her Buffalo roots, her Catholic faith, her business-friendly sensibility — perhaps none is more central than her role as a mother.

“Does anybody not know I’m a mom?” Ms. Hochul, a Democrat, joked at an appearance last week to celebrate her most attention-grabbing win in this year’s budget: a bell-to-bell ban on cellphones in schools. “I say it every single day: I’ve been a mom longer than I’ve been a governor.”

She built on this message in an op-ed published on Friday by Fox News, invoking her status as New York’s “first mom governor” to pledge her commitment to protecting children.

“We’re taking back our classrooms and giving kids their childhoods back,” she wrote.

The message, and her choice of a conservative news outlet to deliver it, was a striking example of how Ms. Hochul has embraced a kind of “family values” approach more in line with the Republican Party of the 1990s than with the Democratic Party of the 2020s.

Indeed, in crafting the cellphone regulations, the Hochul administration found itself following the lead of Republican-led states like Louisiana and Florida, rather than Democratic-led states like California, where regulation is more flexible. Last year, when the governor embarked on a push to restrict social media companies, New York found itself looking to Utah, where the push to restrict children’s media led to the banning of books by Margaret Atwood, Rupi Kaur and Judy Blume.

Ms. Hochul is expected to face a difficult re-election challenge next year, with potential candidates from both parties considering taking her on. They include Democrats like Representative Richie Torres and Ms. Hochul’s lieutenant governor, Antonio Delgado, and Republicans like Bruce Blakeman, the Nassau County executive, and Representative Mike Lawler.

Representative Elise Stefanik, a close ally of President Trump, has also expressed interest in running, and could be a particularly formidable adversary, pitting Ms. Hochul’s Democratic conservatism against the fractious energy of Mr. Trump’s MAGA movement.

Ms. Stefanik criticized Ms. Hochul’s $254 billion budget for not doing enough to address violent crime, calling it a “desperate attempt to shore up a politically weakened and toxic governor.”

Ms. Hochul also has detractors in her own party. Her tendency to align herself with business interests and law enforcement irks some Democrats, while some state lawmakers grumble about her “because I said so” negotiating style.

Facing middling poll numbers and a persistent perception of weakness, Ms. Hochul has sometimes sought a foil in Mr. Trump, issuing stern condemnations of his policies and his attempts to eliminate congestion pricing.

Against that backdrop, it is perhaps notable that Ms. Hochul has sought to humanize her image, asking for voters to see her as a mother. Her team insists that the maternal instinct underscores her vision of what a governor should be: someone who keeps New Yorkers safe, with a roof over their head; someone who makes sure that their children eat breakfast, and who keeps those children from texting in class.

In a state where more than a quarter of voters are not registered with either major party, Ms. Hochul knows she will most likely need to win support from people who may be turned off by politics but are open to hearing from a “mom governor.”

The instinct is written across Ms. Hochul’s legislative priorities, from affordability to public safety.

This year, she pushed to make it easier for the police to remove people having mental health episodes from public spaces, built on her efforts to make New York’s bail law stricter, and gave prosecutors more leeway in turning over evidence to defense lawyers.

Her protective instincts are also visible in her cautious approach to the state’s finances and investment in reserves, which have reached their highest level in years. (This year, she will tap into those savings, to pay off businesses roughly $7 billion in Covid-era unemployment insurance debt, amid fears of a recession.)

But her maternal worldview is perhaps most evident in Ms. Hochul’s use of the state budget to pass initiatives tied to children’s well being. She expanded the child tax credit to $1,000 for children under 4, and allocated enough money to offer free breakfast and lunch for students from kindergarten through high school.

Last year, the governor regulated the use of so-called addictive algorithms that target children, and created a privacy provision that prevented social media companies from collecting children’s personal data.

Ms. Hochul has framed her actions in broad, parent-friendly terms, saying it is a moral imperative to address the increase in mental illness and the degradation of attention.

Yet in one key matter, Ms. Hochul decided against using her influence to compel private schools to provide a basic education. Instead, she included budget language to weaken state oversight over private schools.

Ms. Hochul defended the move as necessary to preserve religious freedom in New York. The change was a priority of ultra-Orthodox and Hasidic legislators representing yeshivas, which collect millions of taxpayer dollars but do not always provide a basic secular education.

The change was panned by Ms. Hochul’s own education commissioner as well as many Democratic lawmakers, who called it a politically motivated betrayal of the state’s responsibility to children.

On the Senate floor, Senator Liz Krueger, a Manhattan Democrat, called the provision “antisemitic” in that it would deprive Jewish children of a basic education, adding that the change could lead to greater erosion in education.

“With this change in law, we’re actually saying here in New York, if you define yourself as a religious school and you aren’t meeting our most basic, sub-minimal standards for actual education, come on down,” Ms. Krueger said.

But in New York’s ultra-Orthodox communities, a potentially crucial demographic for Ms. Hochul come 2026, the move was celebrated as helping to secure “freedom of education.”

A spokeswoman for the Department of Homeland Security suggested on Saturday that three Democratic members of Congress might face assault charges after a confrontation outside an immigration detention facility in Newark during the arrest of the city’s mayor, even as new details emerged that appeared to contradict the Trump administration’s account of the surrounding events.

The three lawmakers — Representatives Bonnie Watson Coleman, Rob Menendez and LaMonica McIver of New Jersey — were inside the facility on Friday for what they described as a congressional oversight visit, which they have the right to conduct under federal law. The facility, Delaney Hall, received its first detainees last week and is eventually expected to hold as many as 1,000 migrants at a time.

Soon after the legislators left the building on Friday afternoon, Newark’s mayor, Ras J. Baraka, was arrested by the head of Homeland Security Investigations in a brief but volatile clash that involved a team of masked federal agents wearing military fatigues and the three lawmakers. He was then taken to a separate federal Immigration and Customs Enforcement facility in the city and released five hours later.

Precisely what led to Mr. Baraka’s arrest on federal trespassing charges, in a public area outside a facility that is owned by a private prison company, remains unclear. But much of what unfolded was recorded by journalists, as well as by cameras worn by law enforcement officials and videos taken by activists protesting nearby.

Tricia McLaughlin, the Homeland Security spokeswoman, told CNN on Saturday that a body camera video showed “members of Congress assaulting our ICE enforcement officers, including body-slamming a female ICE officer.”

The episode was under investigation, she said, and charges against the three lawmakers were “definitely on the table.”

But videos the Trump administration released to Fox News appeared to be far from conclusive, and accounts of the confrontation from witnesses and the members of Congress differ in significant ways from the government narrative.

On Friday, after Mr. Baraka’s arrest, Ms. Watson Coleman, 80, described being “manhandled” by agents who were attempting to arrest the mayor, who was at the center of a large group of aides and supporters in front of the gates to Delaney Hall.

“There was just consistently, and across the board — especially with the folks in uniform — no respect for who we were and no respect for the mayor,” she said Saturday on MSNBC.

In February, the Trump administration entered into a 15-year, $1 billion contract with GEO Group to turn Delaney Hall into a large detention center as ICE rushed to expand its detention capacity nationwide to meet President Trump’s mass deportation goals.

Newark officials have since argued in federal court that GEO Group, one of the country’s largest private prison companies, is operating without a valid certificate of occupancy. After Delaney Hall began housing detainees last week, Mr. Baraka, a Democrat who is running for governor, began showing up regularly and requesting that he and fire officials be allowed to enter and inspect the facility.

Each time, the facility’s personnel turned them away and fire officials issued tickets for code violations.

Federal officials and a GEO spokesman said the mayor had ignored established processes for requesting entry. They have also said that the facility had all the required permits, and have described the mayor’s repeated visits as a political stunt.

On Friday, the dispute escalated significantly.

That morning, Mr. Baraka said he stopped by Delaney Hall to request entry, was denied and left to take one of his children to school. He returned hours later for a news conference that the three lawmakers had planned to hold after touring Delaney Hall.

A security guard opened Delaney Hall’s locked front gate and allowed Mr. Baraka to enter, but barred him from joining the congressional representatives inside, Newark officials said.

“If I was on that property, I was invited there,” Mr. Baraka said Saturday in Newark. “Somebody allowed me. I didn’t climb the fence, I didn’t kick the door down.”

He and several aides waited for more than an hour inside the perimeter of the detention center before he was asked to leave, according to Mr. Baraka and two of his aides.

By that point, Mr. Menendez, Ms. Watson Coleman and Ms. McIver had left the building and were standing near the mayor, according to a video taken by Viri Martinez, an immigration activist who witnessed the arrest.

After several requests that he leave, Mr. Baraka complied, according to two members of his group and video recordings.

“Guy told me to leave, I left. I’m gone,” Mr. Baraka said Saturday.

However, more than a dozen federal agents went out through the gate and arrested him anyway, placing him in handcuffs and leading him away.

Alina Habba, the acting U.S. attorney for the District of New Jersey, has said that Mr. Baraka was arrested after he “committed trespass and ignored multiple warnings from Homeland Security Investigations to remove himself.”

Ms. McLaughlin described the chaotic scene as a “mob,” with the lawmakers, their aides and federal law enforcement officers jostling just outside the facility’s gate.

“We weren’t trying to start anything,” Ms. Watson Coleman said on MSNBC. “We weren’t trying to do anything. We were trying to protect the mayor from what we thought was an unlawful arrest.”

Footage from a body-worn camera shared by Fox News shows the legislators and a scrum of officers outside the facility’s fence. At one point, Ms. McIver appears to make contact with a law enforcement officer in fatigues and a face mask.

A second video also shared by Fox News captures a verbal disagreement between Ms. McIver and several law enforcement officers. Ms. McIver, who is standing with her back against a car and is surrounded by officers in tactical gear, can be heard saying, “Ma’am, he just assaulted me.”

In the video, she and Ms. Watson Coleman walk a few paces away before Ms. McIver stops and turns to face the officers.

“You can’t talk to a congresswoman like that,” she says. “You will pay.”

Mr. Baraka has pushed back against the government’s characterization of the moments before and after he was taken into custody.

“This is all fabrication,” Mr. Baraka told reporters on Saturday. “They get on the media and they lie and lie and lie and lie.”

He said the roughly five hours he spent in custody, before a federal magistrate judge ordered him to be released, were “humiliating.”

By Saturday, Mr. Baraka’s arrest had become a local political flashpoint.

Two of Mr. Baraka’s Democratic opponents in New Jersey’s race for governor — Sean Spiller, the president of the New Jersey Education Association, and Representative Josh Gottheimer — showed up early Saturday at Delaney Hall and spoke to reporters. The three other Democrats running for governor — Representative Mikie Sherrill; Steven Fulop, the mayor of Jersey City, N.J.; and Steve Sweeney, a former State Senate president — also condemned Mr. Baraka’s arrest in statements.

“This is not who we are as a country, certainly not who we are as a state,” Mr. Spiller said at the detention center. “Because right now, we know that folks are scared.”

Mr. Gottheimer added that he and Mr. Spiller were not there as competitors in the June 10 primary.

“We’re here as protectors of democracy,” Mr. Gottheimer said. “We all have to stand up and say to Donald Trump, ‘I don’t think so.’”

Mr. Baraka seemed amused by the candidates’ robust expressions of solidarity.

“I’m glad that they are, you know, making the most of this,” he said with a chuckle.

Across the Hudson River, several New York City lawmakers and Democratic mayoral candidates joined more than 100 protesters at a rally in Lower Manhattan. Speakers praised Mr. Baraka and condemned the city’s mayor, Eric Adams, for working with the Trump administration.

“When they come for the mayors, it’s already pretty bad,” said Brad Lander, New York City’s comptroller who is running for mayor.

Another candidate for mayor, Zohran Mamdani, who represents Queens in the State Assembly, also spoke.

“What Mayor Baraka has told us,” he said, “is you cannot fight extremism with moderation.”

Mark Bonamo and Nate Schweber contributed reporting.

Five mornings a week, Dr. David Slotwiner, the chief of cardiology at NewYork-Presbyterian Queens hospital, can be found tending to human hearts.

But on Sunday mornings, he is on a grass-covered field at a rural farm in Hackettstown, N.J., standing among half a dozen sheep, whistle in hand, teaching his Border collies Cosmo and Luna to herd.

“It helps me think about what it takes to be an effective leader, though doctors don’t respond to whistles very well,” said Dr. Slotwiner, 58, who specializes in cardiac electrophysiology.

He started coming to the farm during the coronavirus pandemic, after Cosmo began showing aggression and bit his wife, Anne Slotwiner, 60. A trainer recommended a small sheep farm in New Jersey, Wayside Farm, that trains Border collies — and, once he herded with Cosmo for the first time, he was hooked.

Dr. Slotwiner shares a three-bedroom house in Pelham, the oldest town in Westchester County, with his wife, Cosmo, Luna and a 15-year-old American Eskimo rescue, George. (He has two adult sons, Harry, 28, and Peter, 25.)

SLEEPING IN, KIND OF During the week, I get up around 5 a.m., but on Sundays, I’ll sleep until 6:30 a.m. I’m not a morning person, but I’ve been forced to be a morning person. I’ll start the day by reading The New York Times on my iPhone in bed.

RISE AND RIDE I go to a 7:30 a.m. SoulCycle class in Bronxville. It’s always timed to the rhythm of the music, which makes it different from other spin classes. Before the pandemic, I was often taking six classes a week, which was not healthy.

MORNING MEET-UP Around 9 a.m., I meet my wife for breakfast at Caffè Ammi in Pelham. She’ll have the dogs in her car, because my car isn’t quite big enough to take them out to the farm in. I’ll get a large whole milk latte with one sugar and a warmed-up cranberry scone and — if I’m feeling decadent — an almond croissant.

OUT TO THE FARM I drive about an hour and 15 minutes to Wayside Farm. I’ll listen to a podcast on the way — I love “Hard Fork” and the NewYork-Presbyterian podcast “Health Matters.” And I really enjoy John Mandrola’s “This Week in Cardiology.” He’s a bit of a curmudgeon and always is slow to adopt new technology, and so I like to hear his critical perspectives. I tend to be a little bit of an earlier adopter, but I like to hear the science of both sides.

WHISTLE WHILE YOU WORK We arrive at the farm around 11 a.m., and I grab my whistle and put on my headset — the distances are very great across the field, so this is how I can hear the people training me — and head out on the field with Cosmo and Luna.

Gene Sheninger and Teri Rhodes, who own the farm, train people to the highest level of competition internationally, but they’ll also take novices. There are other herding breeds, but Border collies tend to be the most common and tend to be the best for sheep.

BABY STEPS The first thing you teach them is to go clockwise, which is called “come by,” or counterclockwise, “away.” And then you teach them to drive the sheep to you in a straight line, in a controlled way, so they don’t push the sheep so quickly that they scatter. And then you teach them to push the sheep beyond you, which is one of the hardest things to get them to do, because Border collies want order — they don’t want the sheep to escape.

The ultimate challenge is to teach the dog how to separate the sheep into two groups, because the sheep instinctually want to stay together as a herd.

TOOLS OF THE TRADE Once you’re a certain distance away, you have to give commands using a whistle. In competitions, sometimes you do this over 800 or 900 yards, where you can’t even see the sheep. But the dogs learn to trust you so much that they know that if you give them the command to go clockwise, even if they don’t see the sheep, they will go clockwise to the edge of the field and keep running and running and running until they find those sheep, and then they will bring them to you.

NEWBIE NOSTALGIA It’s great to be a novice at my age, because I’m teaching medical students and residents every day. I’m teaching attending cardiologists how to do invasive procedures. It’s refreshing to be a beginner at something, to remember how it is to learn as I’m teaching people.

GETTING IN THE ZONE I’ll pack up around 12:30 p.m. or 1 p.m., then hop into the car and finish my medical podcast on the way back to Pelham. It helps me get in the mind-set for work.

DUMPLING DETOUR If I’m on call at the hospital, which I am every fourth weekend, I’ll head to downtown Flushing to grab a bite to eat before my shift. I love the soup dumplings at Juqi.

DR. BOW-TIE WILL SEE YOU NOW I arrive around 2 p.m. and change into scrubs. I’ll usually have four or five patients to check up on, and then I’ll take care of some paperwork or review a manuscript or two.

I’m typically rocking a bow tie. Fifteen years ago, a patient gave me one, and I decided I’d give it a try. It took me a while to figure out how to tie them — it was a lot of YouTube videos — but then I would wear it occasionally, and my patients really liked it. So then I went all in on bow ties. I have more than 50.

DINNER DATE Around 5 or 6 p.m., I’ll head back to Pelham to pick up my wife, and we’ll meet our son Harry and our daughter-in-law for dinner in Williamsburg. One of our go-to places is Ringolevio. If I’m splurging, I’ll have a skirt steak and a glass of red wine. Or I might meet my parents, who live in Battery Park, at a Greek restaurant down the block from them, Anassa Taverna. I love the grilled branzino, with white wine.

FUN WITH FRISBEES You can’t just come home to Border collies and say, “OK, it’s time to go to bed.” They’ve been herding for an hour and a half to two hours, and they’re working hard. So I’ll come home and play Frisbee with Cosmo and Luna for around half an hour. Cosmo is very toy motivated. Luna mostly wants affection and interaction.

KINDLE TIME I’ll climb into bed around 11:30 p.m. and read for half an hour on my Kindle. Right now I’m reading a Tana French novel, “Faithful Place,” which I’m enjoying. It’s a book to clear my brain. I’ve also finished another book that I really love, Barbara Kingsolver’s “Demon Copperhead.” I love the feature where you can switch between reading on the Kindle and listening to it, because that way, when I commute, whether it’s to work or to the farm, I can continue it.

OUT LIKE A LIGHT I usually fall asleep close to midnight. I’m a night owl. But I don’t go to SoulCycle on Monday morning, since I’ve had the whole weekend to exercise, so I don’t have to get up until 6.