I have two DDs, 3.9yo and 12mo, and am a full time primary teacher luckily working in a school in the next village to mine. MIL has them four days a week, doing preschool pick up and drop off for the eldest and having the youngest all day. She works on a Wednesday, so on that day they go to a 7.30-5pm nursery in another village.
Do as much work as you can in school. I don’t know how it works in secondary, but I get in at 7.30 so I can get everything prepped for the day, then mark at break and through lunch and do admin/classroom tasks/meetings after school. I then leave at 4.30pm, collect the children and don’t start work again until 7pm when they’re in bed. I work 7-10pm 4/5 nights a week but never work weekends unless it’s report season, in which case I go to a cafe for a couple of days to bash them out and DH has the children. Evenings are for planning, resourcing, slides etc. PPA is for subject leader stuff - I’m on UPS in a OFE so have lots of extra responsibilities.
DH does all cooking, food shopping and house maintenance. He works FT 7.30-4, so gets the dinner started when he gets home and while I put the children to bed. They’ve eaten at MILs/nursery. We then eat and he clears up while I work. I normally put a load of washing on every morning and put it in the dryer in the evening. Everything goes in the dishwasher. DH deals with packed lunches for preschool and himself, I get cheap school lunches to eat while I mark. Proper clean done at the weekend.
Re the non sleeper, all I can say is it’s a game of survival. DD1 was bad but in a twice a night kind of way until she was 18mo and stopped napping. DD2 is going for a world record in non sleeping and some days last term I was teaching on <3 hours sleep. DH does what he can but the youngest is superglued to me and just shrieks MUMMEEEEEEED if he goes near her at night. She’s currently on 4-9 wakes per night. I mainline caffeine to keep me on the ball enough to function un the week, then collapse and DH runs things at the weekend. Weirdly my performance at school hasn’t been affected, but life admin does suffer, e.g. forgetting MOTs. However, I know from experience that this is a short term thing and by the time she’s DD1’s age we’ll be able to deploy the Gro Clock and a stairgate on her door.
Safly I think career progression can still be affected by children. I’ve turned down encouragement to apply for the deputy role twice in the last three years due to not wanting to give up more of my time to work. Hopefully the opportunities will still be there when the children are older. And, as I always tell myself, I’m trying to set the girls a good example by having my own career and money!
Best of luck OP; teaching can be both a wonderfully family friendly and terribly family unfriendly profession, but it’s doable.