Just some random observations and thoughts:
It seems pretty clear that your Mum won’t be persuaded to move to a 2 bed place where you could be a joint tenant (obviously the one bed suggestion above is totally unworkable), and that if you move into her present home with her you will have to leave when she dies or goes into a home. The council may rehouse you or they may have no acceptable accommodation suitable for a single person so that’s a huge gamble.
You say you live 80 miles away and you are going to have to find somewhere else to live before long. Your landlord is probably hoping that you will move without the expense of her serving notice and going to court but unless you have found another suitable place in the meantime don’t move out until the landlord has obtained a court order and the bailiffs are due to turn up.
You don’t mention work. Do you have a job? Would you be able to find another if you moved away from your current area? Would your mother expect you to stay at home with her all day? Or are you reliant on benefits?
Do you have friends in your current area, a social life that you would have to leave behind if you moved? If you moved in with your mother would she want you to be there all the time to keep her company, thus making you become very isolated?
Do you actually want to become your mother’s carer? And is that really practical as you’re a man? Would either of you be comfortable with your undertaking some quite intimate care as time goes by? Taking your Mum to the loo and cleaning her afterwards for instance? Even if she is able to get carers to come in a couple of times a day for washing and dressing when that becomes necessary, you would have to deal with night time care. She will over time only become less mobile and capable and could live for another 20 years. I wouldn’t even want my husband undertaking my personal care, let alone my son!
I’m afraid this is really just a lot of questions but you probably sense that my advice would be to find alternative rented accommodation in your present area, not to move away and live with your mother. You are relatively young whereas, sorry to be blunt, your mother has had her life and is thinking only of herself and what she wants. She’s not thinking about what is in your best interests so that’s what you need to do, because nobody else is going to. You owe it to yourself to live the best life you can, not to become an elderly woman’s carer and find yourself when you are her age homeless, friendless and living in poverty. Your mother could, but won’t, move into sheltered accommodation or a home. That’s her decision. You are not her only source of help and companionship.