if the person is on a maximum care package it doesnt mean the next step is a care home at all, it just means that supplementary care or tasks or interventions or errands need to be done by family and friends.
Social services can't force anyone to provide that care. If nobody is willing to do it (they don't need a reason, just "no" is enough) and the person's needs can't be met with 4x care visits a day then they absolutely do qualify for going into a home. And that is what happens because it's the most cost effective option for social services versus providing even more carer/support worker hours (support workers are who does all that other stuff you mentioned, where people have no family or friends to help).
You're right it's not easy because social services will tell you lies and say you have to provide care or they aren't going to provide care etc, none of that's true. The hardest part is that the person might suffer a while temporarily until social services realise you mean business. Social services won't step in because you want to stop caring. All the time you're doing it, the person's needs are met, so they aren't eligible for further social services funded care. You have to notify social services of your intentions to stop caring and then stop caring first when you said you would, so there's an unmet need, before they'll step in.
It's not easy getting social services to do their job but it is an option. Where someone is being run ragged to the point that something needs to give, it's perhaps a sensible option, rather than the person's children suffering or the person's own health going downhill or having to stay in a marriage they'd prefer to leave, because they've no time to work to support themselves etc. Maybe it's not an option OP wants to take, but it's important she knows it exists. If she's caring for her relative it should be through choice, having weighed up the pros and cons, not because she thinks she doesn't have any choice. I understand the law around it perfectly well.
Im not sure why people have repeatedly gone on about driving when OP has set out a number of times that she has chosen not to continue trying to learn to drive because she couldnt get on with it.
Probably because the second half of her statement was that he wouldn't pay for any more lessons. Until her most recent post where she clarified a few things about it, it wasn't sounding much like it was her choice. And she has DC with SN which most people would find to be a lot easier to get them from A to B in a car than on public transport.
It also opens up opportunities for work, both in terms of location and in terms of distance able to be travelled in a certain timeframe. You can often do 30 miles in a car in the same time it takes to go less than 10 miles on a bus. In some areas, running a car can be equal to or less than the cost of public transport too (excluding the initial purchase price). She mentioned having limited time to work, a car would help with maximising that. If it's not something she wants to pursue for whatever reason then fair enough, but that's not how she initially made it sound.
OP nobody is really going to be considering all the "what iffs" when you post. Usually people will take what you say at face value. So if you only provide part of the information, you can't expect the same responses as if you provided all the information and people had a complete picture.