OP, first of all, I understand.
When DC2 started school years ago, there was NO bus at all,other than a terrible out of the way route which required three buses and took and hour and a half (it was a route where a bus came every half an hour- this just isn't realistic). So really, only walking was an option. I don't drive and we only have one car which DH uses and needs (he deals with urgent situations which require him to be available quickly and at any time). I couldn't cycle because the terrain was all mud and stone AND the bridge to cross over was just too tricky with two small kids in tow. Believe me, I plotted and schemed but couldn't find a better way, other than walking. Our walk was 45 minutes each way and it wore me down. You can't do taxis. That was always suggested to me. "Can't you just Uber?" No because actually, £14+ a day on taxis is not doable.
We put our daughter on a waiting list of another school at the end of year 1. By January of year 2, she moved. It was a great move! Ok, so here's the thing, the school is still far away (not as far) but it's right next to dad's work so he drives her and brother in every morning and I pick them up by bike every day (I have a tricycle with a bench on the back for them to sit on). I love it! I love cycling and the route is mostly tow path, so very little traffic. 20 minutes and we're home. And even in the cold winter, it's great. They just bundle up with flasks of hot chocolate, hats, gloves, and decent coats. It's such a calm way to travel.
Can you cycle? Is there a nice route? Can you invest in a box bike or something?
Home schooling is a big decision. It's a total lifestyle that you need to plan and execute without stress being the motivating force behind this decision. I was home schooled for a year by my mother who had been an English Lit secondary school teacher and a head teacher. She managed it very well and stress wasn't the motivating factor behind her decision. And it was always going to be one year: Year 4. Then I returned to school for year 5.
It might work in this case: put your kids on waiting lists and home school them in the meantime.