I have seen lots of stress on Twitter and think pieces in the news about working with kids at home. I've learned a few lessons on this topic while using minimal daycare during the four years prior to my new position at the University of Minnesota last semester (one year was my final in graduate school and then three were on the tenure track). I had, in the end, two small kids, between the ages of zero and four during these years. There was one semester with two days a week, two hour child care (graduate school), one semester with five hours a week of childcare, and one semester with six hours of babysitting. Otherwise, we were DYI. Now, I'm in a two-body problem academic household. So my advice really only holds when there are partners around and both have some flexibility to their schedules. Take what you will from this. My advice obviously won't apply to all situations. Below, when I say "you," I'm generally talking about rules that worked for my spouse and me.

Oh, and in a follow up post, I will discuss how this global pandemic / potential economic collapse feels a heck of a lot different than my previous years of intensive childcare, and how I have struggled (...or maybe more accurately...failed) to follow through on some of the advice below.

Schedules

You must make a schedule and stick to it, almost no matter what. You are near a breakthrough in your writing, but it's your partner's time to work? Too bad. Hope you remember it when you're back on the clock. Lowers resentment, increases fairness.
Your work is now defined by hours, not tasks. It's easier, in my opinion, to let hours fill into your tasks to complete them. Now, the minutes tick away. And you either do or don't get your stuff finished in a finite amount of time. It's a mindset change.
There are 24 hours in the day. You're now in a situation where ALL are on the table for appropriate work time. Our schedule typically went from 4am - 6:00pm devoted exclusively to switching between either childcare or work. Right now, in response to covid-19, our schedule stretches from 4am to 7pm. It's painful, but is what needs to happen for us to cram as much into the day as we can.
Severe reciprocity. You have a newly scheduled hour-long meeting pop up that absolutely CANNOT be moved, but that is in your partner's time? This might mean that you don't get to linger at the end of the meeting. And it might mean that you cook dinner tonight solo and don't get to shower before passing out into bed. But you MUST give an hour back to your partner if you take one.
Don't count on long periods where you make little breakthroughs. Work isn't a long drink of tea throughout the afternoon. It's a shot of espresso. You must lock in, focus, and you'll likely feel fatigued at the end.

Expectations

I became EXTREMELY uninteresting over those four years. I worked, spent time with my kids, and slept. That's it. To your new favorite tv show, say "thank you for your service." I transitioned to watching one or two five-minute Youtube clips before falling asleep. I love myself and I love my family, but I had to BS when people on job interviews probed my cultural capital and leisure activities.
We had a break at Christmas, and for a few weeks over the summer while we visited family. But don't hold a carrot of imminent change in front of you. Get used to the situation.
There are seven days in the week. They're all on the table to do the three things you must do: work, childcare, sleep.

The actual work

You need to change yourself to fit your new restrictions. You can't change your schedule to fit your preferred working habits. You're hour based now. Get 40 hours in or as close to 40 hours as you can, anywhere. If you can't get all your tasks done in 40 hours, that means you need to change how you work. Faster, more efficient, more forgiving of typos, less productive than what you'd like.
You're hour based now. I've heard, and seen, people taking breaks on the job -- chatting with colleagues, watching youtube, reading twitter, doing non-core work activities, lingering. Now that I've been task-based for awhile, I've started to do this too. You can do that, but you won't get the things done that you must absolutely get done. This feels really bad, and in many ways it IS really sad, but say goodbye to those non-core things.
You must, must ... MUST say goodbye to the internet and to the social media. Or at minimum, you must rigorously schedule them, and keep timers going when you're using them. Use harsh, unforgiving accuracy when measuing the amount of your day that you view the internet.
Lists are your friend. I like to spend 5 minutes beginning and ending my work time centering myself on what I need to do (at the start) and what I did do (at the end). I use the program Workflowy and love it.

Happiness and emotion management

Draw a bright line between childcare and work. Don't blend. If you must blend, then you must recognize that you are leaving your children unattended to do work. That puts the proper weight on your decision in this new arrangement.
To the best you can, be in the moment. When you're working, you must work. When you're parenting, you must parent. We both found that mixing tasks while living this strange blended life caused anxiety, sadness, and problems.
This may just be me, but while I was in a more isolated situation, the internet and social media made me feel sad, paranoid, resentful, and mad. I also recognized that I checked it out of compulsion to manage my worries, anxiety, and feelings of loneliness (it of course did not resolve any of these feelings). I found the casual use of internet/social media to be especially problematic in this situation.

It's not all bad!

The four years of intensive childcare were probably the happiest of my life. And I had some very happy times prior to them! It's super hard, but it also feels super meaningful and rewarding.
You'll be more likely to be around for very important parts of your kids' lives. For example, my son took his first steps to me on a random Wednesday afternoon in 2018. I'm very happy to have been there.

I haven't talked much publicly about this experience. I typically fibbed about my childcare situation for fears of being viewed as uncommitted to my work (lots of thoughts on this...). There are strong norms in my field of viewing academic work as a calling and a passion. There are lots of jokes about how work is better and easier than childcare. I'm in a much more privileged position than most others to violate these norms, but I still sensed the importance of conforming to these occpuational expectations. But now that many of us are in this new strange boat, I thought these lessons might help smooth your transition into the weird world of blended home/work.

Please, be good and generous to yourself and others. Take good care of yourself.