It's almost half term, use the time away from the classroom to consider your options.
Book the kids into childcare for a day, go see a solicitor and get your options. Then go sit and have an hour in a café and think about what you want. Not what is best for anyone else, what you want. Then think about how you can achieve that.
Teaching is all encompassing at the moment, I have 2 friends who are considering their future in teaching because of the insane workload and they have very supportive partners, I honestly don't know how you are doing it.
Some options to make your life easier:
Have you checked if there is a childminder who would do the school run, cutting your drop offs to one on a morning? I offer before school care and some of my kids are dropped in their PJ's and we do breakfast, teeth, sort hair etc and then I drop them at the school bus.
Can you move closer to school? Either yours or your child's? I honestly don't care if it makes your husbands life more difficult, he can put up of fuck off.
Arrange a meeting with your HOY and SLT to discuss some extra support. There might not be anything available but they should at least be able to offer some advice on how to manage the workload.
On the days he's at home with the kids, stay later and do marking / prep. He needs to handle it. Tell him you are putting your phone on silent, get your head down and plow through. You'll get more done between 4:30 and 6 than you will at night because you won't be seething with resentment, be worrying about all the house things you need to do and be breaking off for things. I'm guessing he regularly disturbs you when you are working, either with silly requests, pointless interruptions or making stupid noises while playing his games.
Have a chat with your union. See what support they can offer.
Finally, do you have any family you can go stay with in half term for a day or 2? Ask them for support, be clear why you are asking.
Don't cover for his laziness, make excuses for him or any of the things I'll bet you usually do.
Oh, and google how to cut wires internally on a playstation. Someone somewhere must know how to break one without making it obvious it was you.