OK, so that gives one practical thing you could address. Asking someone to do antisocial hours both ends of the day like that would be unreasonable whatever the person's situation. Can you bring that up with work? Explain that you are totally commited but in this unusual situation cannot do both the early and late shift?
I have a 7 year old and she has been on screens a lot and has gone a bit peculiar as an only child (she was a bit peculiar to begin with!) She constantly asks me to play Roblox and a couple of weeks ago I cracked and joined her. It was actually quite relaxing. I guess if you can't beat 'em join 'em. I've been surprised by the excellent quality of today's kids' TV too. I've got a bit hooked.on Operation Ouch. Anyway...
Your DD is a free reader. That is terrific. All I did at her age was read but you know, if I'd had an iPad I jolly well would have been on it (hours of programming a ZX Spectrum were probably educational, but I liked the games more).
To take a long view, I was thinking as I read your post about my parents, who were born in 1938 and 1942. My Dad mentioned in passing recently (I was doing research to write a speech for a big birthday) that they were bombed out of his house when he was 4. They had to move in with his aunt, uncle and cousins. For a year. 8 people in a 2 bed house.
My point is that my parents had a really suboptimal childhood by today's standards but they have led long healthy, productive lives and while I don't know for sure their parents didn't feel guilty, I'm guessing they didn't feel WWII was their fault.
The pandemic is not your fault either and DD will be ok. Now get working on that employer.
I have a good employer but there have been numerous times over the years that they've been oblivious - for example, that holding twilight training or meetings on the same day each time will impact the same workers (now they hold some meetings at lunchtime and vary days).
Look for a new job too. You must be the most efficient person ever after the last few months.