It took me almost four years of weekly 2hr lessons to learn.
My first lesson covered pulling out from being parked on the left of an almost empty, wide street, and pulling in to the left again. I was really anxious and screamed (quietly!) a lot.
Progress was slow, obviously.
It took me 4 attempts to pass my test, over six months.
Once I'd passed my test (aged 38) I took myself off for short, familiar drives, with lots of pulling over and parking (used the easy streets I'd first learnt on). Talking myself through everything out loud. Had to really push myself to gradually go longer distances, and would be drenched in anxiety sweat every time.
About six months after having my own car I realised I was basically driving as normal without it being so terrifying. (Also realised that once I got over the fear of speed, motorway driving was easier/simpler than around town.) After a year I realised I was doing everything automatically and somewhere along the line it had just clicked. I kept my P plates on until this time.
Just explaining the timescale it took me.
You are doing so brilliantly with so much in your life, it's so sad that you can't see that. Not only a single mum, but both kids with additional needs, and yourself likely with undiagnosed additional challenges! You're managing so much so well every day. If you are neurodiverse yourself, you have likely spent a lifetime having people make out you're not doing well enough at one thing or another - this may explain the heartbreaking lack of confidence and the way you are beating yourself up for finding an incredibly difficult situation ... incredibly difficult.
I think going to local councillor, and failing that, MP, to sort SN transport is the best option. Many parents can't drive for various reasons so there has to be an option, and if there isn't they need to make one.
This will take the pressure off, and you can keep learning to drive in a more relaxed way, and get there in your own time.
I cannot stress how much I thought I wouldn't be able to learn, and how weird it was when I realised I was doing it!