It's really good to have found this thread. Pennies - I sympathise. It sounds as if you have a lot to deal with here. I don't have much practical advice, I'm afraid, but can share my own experience.
At the moment, my MIL (81) is living with us. She is in my DS2's bedroom and my two sons are sharing a room. Her home is an hour and a half away from us and she had always said that she would move near us if her husband died. He died five years' ago. She didn't move. We took her lots of estate-agent listings on flats and sheltered accomodation, but she took no notice. In fact, she started redecorating her house, although she refused to have central heating put in, so she was always freezing in the winter.
We understood that she wasn't ready to move and respected that, but we were frustrated too because we worried that she would leave it too late. She always said that she didn't want to be any bother to us, but my husband (her only child) feared that at some point she would be ill (she already had a lot of health problems) and he would need to fit in driving over to care for her with his work and family life.
Sure enough, a crisis happened. She suddenly became very ill and a neighbour phoned an ambulance. It turned out she had appendicitis (at 80!) and complications. Then she caught MRSA or similar.
There was no way she could return home after this as she was too frail and needed to be looked after, so she has been living with us for the past two months. We live in a tiny house, so this is far from ideal and could have been avoided had she moved here earlier. We have had to transfer all her care (she needs various tests and an operation) to our local hospital, so that we can take her there and look after her afterwards. My husband has had to go onto a four-day week so that he can have time to drive her to all the appointments she needs.
She has now agreed that she needs to put her house on the market and move nearer to us. She has even - finally! - agreed that sheltered accommodation would be a good idea (originally, she wanted a small house
). However, it took this crisis for her to see how vulnerable she was and how much she needed us.
I do think that it is a difficult matter to balance an elderly person's happiness with their physical well-being. With my MIL and my grandparents, I saw standards deteriorating in their houses - cobwebs appearing, dust everywhere, crumbling paintwork - but they were in their home and that was the most important thing to them. My MIL was always houseproud, but she obviously can't see as well as she used to as her house is very dusty these days and her washing up is awful (scraps of food left all over the plates).
So, your mum has a cleaner who is not very good, but she has been cleaning for her for many years. She sounds as if she is a lousy cleaner, but she serves a very important role in providing continuity and company for your mum, so you mustn't rock the boat. So long as hygiene is not compromised, I don't think it matters too much.
Does your mum have any neighbours who can look in on her? My MIL's neighbours were wonderful and it was her next-door neighbour who called the ambulance. If you are lucky enough to have a kindly neighbour who is friendly with your mum and you are in touch with them, this can be a godsend. Failing that, are you in touch with the friend/cleaner? She might be able to keep you informed about your mother's health and well-being.
I'm sorry that you have had a difficult year yourself. It sounds as if this worry over your mum is the last thing you need.