Top of your list has to be your own sanity. You will be absolutely no use to your DD if you have a breakdown.
And remember that a few short focused lessons one on one at home will provide a lot more learning than can be achieved in a large class over a longer period. So there’s no need to aim for anything close to a full school day.
A few things that may help:
Childcare bubble. Either with another family or are there any older kids/young adults you know nearby who would welcome the babysitting money? Not a perfect solution but I’m sure they could manage working through a few worksheets with your DD. Any older kids of family friends?
Decide what’s important for both school and work and drop anything that isn’t towards the top of that list. For school that’s probably English and maths.
Go through the school requirements and pick out any things your DD might be able to do independently. Do they set art challenges? Failing that try and set her up with some creative stuff that you can leave her to it for a while.
If she doesn’t have live lessons you could set some structured educational screen time. Either the bbc bitesize stuff or maths or reading apps. I’d add some YouTube PE into that as well. You don’t have to go for 9am, they’re all available to replay so chose a time that suits you.
Try and carve out some early evening time for reading. I honestly wouldn’t try and catch up anything else once you are done with work, it’s too late for a kid that age to concentrate. But reading before bed is a good way for everyone to calm down at the end of the day.
I like the PP suggestion of pairing up with a school friend over FaceTime so they are trying to do school work together.
You can do some catching up at the weekend but I really wouldn’t go for full on school all weekend. You all need some downtime. Maybe finish the most important bits from the week and then do some games? Scrabble is a great one. There’s a junior version too. Teach her to be the banker in Monopoly. Or some card games? I know they’re not school work but can be great for word and number skills.