It's been a chaotic week as students headed back to school during the latest Covid surge and winter storms, and working parents are stretched thin managing hour-to-hour changes alongside their jobs.

An estimated 5,225 U.S. schools went virtual or closed at least one day this week, according to a school opening tracker from Burbio — some due to rising Covid cases that led to illness and teacher shortages, and others, like in Chicago, after the district and teachers union failed to agree on Covid safety measures. Snowstorms across the mid-Atlantic shuttered schools and care centers as well.

In school districts that remain open, parents sent kids back to classrooms under new and uneven guidance around testing to return, masking in school, isolating after a positive case, moving to half-days and other safety requirements.

After what seemed to be a smooth start to the school year just months ago, many parents say the latest school and work upheavals make it clear they still aren't getting the flexibility and support they need most from employers during the pandemic.

'There's no way any one of us can compartmentalize everything these days'

In New York City, Jeannie Kim, 48, wrote a message on LinkedIn the night before she sent her two kids, ages 9 and 14, back to classrooms on Monday.

"If you've got parents of school-age children on your teams," Kim wrote, "give a thought to the incredible stress they'll be under this week: either sending their kids to school with a mask and a prayer during the worst Covid wave we've seen yet, or once again attempting to work and parent simultaneously while their kids learn at home. Extend a little grace to your reports, your coworkers and your bosses this January."

To be sure, living through the pandemic has been relentlessly difficult for everyone, Kim tells CNBC Make It. As the vice president and general manager of content at Policygenius, she's continuing to lead with empathy as she has for the last two years, but with extra awareness of the hard decisions parents are having to make right now.

"People have really complex lives outside of the time they spend working for you, more than you can recognize," she says. "Allow people to bring that to work with them. There's no way any one of us can compartmentalize everything these days."

Being a thoughtful and supportive manager also requires flexibility, Kim adds, which could mean embracing when a child makes a Zoom cameo, or shifting someone's deadlines if their child's nanny calls in sick.

"We can't take away people's stress," Kim says, "but we can at least not add to it by having them worry about how they're going to get their work done right now."

Businesses must 'redefine what child care means'

Roughly 1 in 4 working parents is experiencing burnout at work, according to a recent survey from Maven and Great Place to Work, resulting in estimated 4.8 million cases of what the report calls "preventable" burnout. But parents are less likely to report feelings of work burnout when they see benefits as special and unique for their needs, believe leaders genuinely care for them as people, and feel treated as a full member regardless of their job role.

Flexible work benefits, namely backup child care, would help parents like Angel Johnson, 43, most. Her 5-year-old daughter went back to in-person classes in Feb. 2021, but rising Covid numbers in recent weeks threw everything into the air again. Johnson says 11 schools in her Silver Spring, Maryland, district have decided to go virtual due to Covid.

Johnson worries about what the coming months could hold for parents and single mothers like her. In 2020, she was able to tap emergency in-home child care through her ex-husband's workplace but won't have that option this time around. She could try a discounted day-care facility, but what if it closes due to an outbreak?

"People are feeling the pain," Johnson says. "It's an extreme pinch on parents of school-age children trying to figure things out."

Carleen Haylett, 46, of Boston, is a single mother to a 10-year-old son and believes businesses must "redefine what child care means," specifically extending options that help older kids who still need to be supervised or engaged in activities while their parents are at work.

To that end, she is the founder of Sit-a-Bit, a tech platform that gives employees online access to K-12 enrichment classes ranging from tutoring to coding to art. Because she has flexibility as her own boss and is tapped into online educational resources, she decided this week to keep her son home from school due to Covid concerns. Now she's considering pulling him out of the public school system for the remainder of the year.

"The anxiety associated with whether or not school will be open or closed, if there's a case in class, do we have to quarantine — it's too much," Haylett says. "I can't live with that cloud over my head and waking up every morning and not knowing what's going to happen."

In Arlington, Virginia, Sean Steele, 46, is on his own looking after his four kids ages 7, 9, 11 and 12 while they're home due to snow and his partner is sick.

But he's better able to manage it all thanks to one new benefit: His company, Infolock, where he is co-founder, started providing unlimited paid time off beginning this year.

Steele says he's made it clear unlimited PTO extends beyond vacations to include days off to manage burnout, sickness, Covid long-haul symptoms and more. "We assume if we support [employees] the best we can, we'll get the best back from them when they're available — not just physically, but also emotionally and mentally."

For emergencies like child-care needs, he adds, "you just take it — you don't have to ask for permission."

Both Steele and his co-founder, also in the Arlington area, are currently taking advantage of unlimited PTO while their kids are home from school.

"I'm going to come back to work when I can," he adds, but making sure his kids are safe and cared for right now "is the most important job I have."

Check out:

4.8 million working parents have ‘preventable’ burnout—here are 5 things that can ease the stress

3 ways employers can better support parents and caregivers at work

Covid vaccine booster shots are here for kids ages 12 and up — here’s what parents need to know right now

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