You're human and you're undergoing a HUGE amount of stress and trauma, both for yourself and with your daughter.
It doesn't matter how great your life or career or DP are: this isn't a scenario that anyone, from the poorest person with no job to the most high flying CEO, is expected to get through without feeling stressed and broken. How you feel is normal.
And all the things a person needs: sleep, food, time to themselves, the ability to reset - they don't magically disappear because something is happening. And you're not meeting at least some of those needs right now because you're doing things for everyone else on top of your immediate need to look after and advocate for your daughter.
So you're burning out, spectacularly. Time to send up a distress flare to anyone who can pick up the load a little bit for you: your partner, your parents, a friend. Tell them you need them to sort the kids' uniforms for tomorrow, do you a food shop, buy you a bottle of wine, do the school run, cook, phone the council about your council tax bill, whatever needs doing. It's not negotiable - you need space to decompress, even a tiny bit, or you're going to keep building pressure to a point where you can no longer be useful to anyone, most of all yourself.
Send up the flare. "I'm not coping, and I need an hour/a night/a day to breathe before I completely lose my shit. I need to be okay to be able to be there for DD, so I need your help, please. I need X, Y and Z doing."
And then sit in your car, or your shed, or wherever you can find space for yourself, and let yourself feel it all. Be devastated and cry and howl and do whatever you can't do in front of DD. Or read a magazine, drink a brew, have a bath, and pretend it all isn't happening for an hour or two, if you think that will help instead.
Good luck. I hear the pain and distress in your words and I need you to know those are normal and you are okay, you will be okay. But you need to make space for that to be possible.