My father has been getting steadily frailer over the last 6 years, both mentally and physically. He is now 83. My mother, two years younger, is still very well, and determined to keep him at home for as long as she possibly can. We have had many late night trips to hospital over the years, and it is only in the last 6 months that she is finally getting the support she needs - as another poster said, the services, social and medical, will avoid doing anything for as long as they possibly can, so far as I can see.
However, she is now organised with nurses coming in three mornings a week to get him up, washed and dressed. The local care team have sorted out a hospital bed (he now sleeps downstairs in the sitting room) and something called a standaid to get from bed to wheelchair to armchair. They have also found her a sort of slimline wheelchair so he can have a shower once a week (the nurses do this). A carer comes in once a week to sit with him so that Mum can get out to choir practice or do a bit of shopping.The doctors surgery has finally got its act in gear, and the doctor and district nurse visit when it is needed.
Having the support in place has made a huge difference to Mum - she can now cope with what she wants to do for him. I have enormous admiration for the kindness and and grace with which she is handling such a horribly difficult situation.
I suppose what I am trying to say is firstly, if your Mum wants to keep your Dad at home there is a lot that can be done to help her. But she will have to be very firm with all concerned that he only comes home when there is a proper care package in place. My mother has been her own worst enemy in many ways - Dad loathes hospitals, and Mum has always done her utmost to get him home as soon as she can without necessarily waiting for things to be sorted out. The cost of getting help in to support a carer at home is infinitely less that full-time nursing home fees (my parents are well-off enough that they are self-funding). So far as I can tell, if your parents have much in the way of capital, most of it will have to have been spent on care fees before the state steps in, but I am not sure exactly what the thresholds are. Your local council website will probably have quite a lot of information about what is available, and will certainly be very up front about who and how they expect to pay for it!