Last month, Dr. Bertha Mayorquin, a New Jersey physician, told her soon-to-be ex-husband that there was a change in plans. After two weeks of providing treatment by video as a precaution against the coronavirus, she would resume seeing patients in person.

But when she left work on a Friday to pick up her two daughters for the weekend, her husband, Wendell Surdukowski, presented her with a court order granting him sole temporary custody of the young girls. His lawyer had convinced a judge that Dr. Mayorquin could expose the children, 11 and 8, to Covid-19.

The doctor, an internist, had intended to spend the weekend celebrating her younger daughter’s birthday. Instead, she spent it frantically assembling 50 pages of paperwork to try to reverse the order.

“Many people working in the hospitals — doctors, nurses, so many of us — are parents,” said Dr. Mayorquin, whose hospital had asked her to starting treat non-coronavirus patients at an urgent care center to ease the burden of the pandemic. “Are our children going to be taken away from us because we are on the front lines helping people?”

That question is arising across the country as a growing number of parents have begun to withhold access to their children from former spouses or partners over fears of infection, according to families, lawyers and judges. For health care or other essential workers, the battles are infused with heightened controversy. Some say they shouldn’t be punished for doing crucial services; their counterparts argue that the jobs pose too great a risk to other family members.

“If there’s an imminent threat to the kid’s well-being, you must take action, whether that’s something like drug abuse or a virus,” Mr. Surdukowski said. “Watching the news, looking at the cases of doctors being sick, you cannot tell me that they are not at a higher risk.” Mr. Surdukowski, who has an underlying condition, had told the judge that he was also concerned about his own health.

Amid the pandemic, the landscape of family law, which varies across the country, has become more uneven, with few guidelines to address the current safety concerns. Families of medical workers aren’t the only affected. Other parents are arguing over who comes and goes from each home, whether children should be on the playground and if travel to more remote areas should be permitted.

“What we are recommending is to figure out a way for visitation to go forward, and if there’s an emergency worker, to figure out how to salvage it as best as you can,” said Susan Myres, president of the American Academy of Matrimonial Lawyers. “We can’t make those people have to sacrifice more, but how do we do that custody safely?”

Some courts have issued administrative orders addressing the coronavirus crisis. For example, the state district court in Davidson County, Tenn., said that the “primary residential parent” should take custody of the child within four hours of a shelter-in-place order and retain sole custody until the order is lifted.

The Massachusetts Probate and Family Court’s chief justice issued an open letter saying it was important that children spend time with both parents who had approved custody agreements. If a parent must self-quarantine or otherwise be restricted from contact, both parents should cooperate to allow time with children by video conference or telephone.

But those orders do not directly address what should happen when one parent is continuing to work on the front lines. The court system in New York, the epicenter of the coronavirus outbreak, has not issued any written child custody guidance at all.

“It’s not like there’s case law or clear guidance,” said Conti Moore, a lawyer who works on child custody cases in Florida. “This is unprecedented. It all boils down to: How do you co-parent in a pandemic?”

When parents do seek help from the courts, they are getting very different responses. Some courts are largely shuttered. Others are holding emergency hearings online. And one jurisdiction’s definition of emergency may not be another’s.

Last week, Tabatha Sams, a client of Ms. Moore’s who lives in a suburb of Orlando, decided she no longer felt comfortable sharing her 21-month-son with his father, Stephen Thilmony, a firefighter. He sought to assure her that he and his fiancée, an emergency room nurse, were taking the proper safety measures, including wearing personal protective equipment while at work. But Ms. Sams had watched with growing alarm as Covid-19 cases swept across the country.

Finally, she reached a breaking point. “I said, ‘I’m not comfortable with the situation,’” Ms. Sams recalled. “I can’t roll the dice.” On her lawyer’s advice, she filed an emergency motion asking a judge to grant her sole custody for the length of her state’s shelter-in-place order.

“There are still first responders sleeping in cars to stay away from their families,” Ms. Moore, the lawyer, said. “It seems only right that the child stay with the parent with the least likelihood of exposure. The courts have to deal with this.”

In a written response, Mr. Thilmony’s lawyers told the court that Ms. Sams had not cited anything specific that he was doing to put their son at risk, and that she was seeking to deny him agreed-upon time with his child after they had battled over parenting issues unrelated to the coronavirus. “The father should not be denied contact by the mother, through the emergency motion, due to his position as a firefighter,” they wrote. Mr. Thilmony declined to comment for this article.

The judge scheduled an online hearing so that both parents could attend and have adequate time to prepare. They will make their arguments on Tuesday.

In New Jersey, Mr. Surdukowski got an emergency hearing the same day his lawyer filed the motion. It was late on a Friday afternoon, and when Dr. Mayorquin’s lawyer could not be reached by phone, the judge issued the order, granting Mr. Surdukowski sole temporary custody.

Distraught at the separation from her daughters, Dr. Mayorquin immediately began preparing to get them back. She ticked off the points: She did not intend to treat patients with Covid-19. She would wear personal protective gear, and change out of her scrubs and shower immediately when she got home. But, in the end, she felt the safest course was to meet Mr. Surdukowski’s demand that she not see any patients in person.

The hospital let her retreat to her telemedicine job. As much as Dr. Mayorquin regretted not being able to do more at a time of critical need, she said she felt she had no choice. “I didn’t want to fight,” she said. “I just wanted my kids back.”

The assurance worked. The next Monday, after an online hearing, the judge reversed the order.

In Monterey County, Calif., Lisa Chu filed an emergency motion seeking sole temporary custody of the 11-year-old twins and 9-year-old son she shares with her ex-husband, Steven Biakanja, a firefighter. He would have to produce a negative result from a coronavirus test every time he was scheduled to see the children — an impossible demand, given the limited availability of screening.

Under their court-approved parenting plan, the children normally spend roughly 60 percent of the time with her, and the rest with him. But two weeks ago, Ms. Chu wanted to withhold the children from Mr. Biakanja after two fellow firefighters tested positive for Covid-19. They and others at his firehouse quarantined at home. Mr. Biakanja assured her that he would self-quarantine if he developed symptoms or had known contact with anyone infected with the virus.

But given the shared spaces in the firehouse and the possibility of asymptomatic carriers, Ms. Chu worried that her ex-husband might unwittingly transmit the virus to their children — or her elderly mother, who visits her home frequently.

“I know this is hard on everyone, but it’s a decision that we have to make,” she said.

As one week turned into two, Mr. Biakanja was increasingly angry. “This is an attack on anyone who is helping with essential needs of this country,” he said.

Then, on Monday night, the children were back with their father. The judge had denied Ms. Chu’s request for temporary custody. Unless Mr. Biakanja exhibits signs of Covid-19, the previous court order remains in place.