OP you say that 'we may in the near future have to move to an area where public transport is not great', can I ask why you would NEED to move to an area like this? Surely if you have to move, you can move where you like, to some degree, so why would you chose to move somewhere where there is no public transport to speak of?
Also, I have to say, that I have NEVER in all my life, and I'm in my 60's, met such a 'Negative Nellie' as you are. Everything anyone suggests, you respond with 'I can't do that', and I mean EVERYTHING! You really do need to change your mindset to have a hope in hell of passing your driving test, people have suggested all sorts of solutions to this, but every time, you say, 'I can't do that'.
The fact that you have two children with special needs, that will need to go to different schools, means that it is highly unlikely that you would be able to take them both, and arrive on time, even if you were the best driver in the world. So I think you need to focus at this point on how you CAN achieve this. There must be other people in your situation who have two kids, that start at the same time, but at different schools, how do they manage? The state can't tell you that your children MUST go to school, and then not provide transport, so in spite of the fact that you say they won't do that for you, I think you are wrong, and just haven't spoken to the right people. However, if you believe, having checked again, that transport won't be provided, then I suggest you email your MP, and ask them for help. Another place to ask for help would be Citizen's Advice. I feel sure that they will help you get the support that you need.
Once you've found a way of getting the kids to school, then, and only than, you can think about learning to drive again, and hopefully with the attitude of 'I CAN DO THIS'.
Sorry if you think I'm being harsh OP, but you really do have to get a grip on the situation, and this negative attitude definitely won't help.