Unfortunately, your mother needs to be made to realise that the “option” of staying in her own home with you looking after her is NOT an option (for all those reasons you have listed in your first post).
Her two real options are to (a) stay in her own home with the help of carers, or (b) move into residential care.
As you have been living with your mother - and are over 60 - her property should be disregarded when calculating what she would have to pay for her care.
You say that she could afford residential care - is this because she owns her house (and you would be willing for this to be sold), or because she has substantial savings?
There are so many misunderstandings about paying for care.
I had a long battle with Hampshire County Council who didn’t follow the rules, and they (grudgingly) refunded mum £8,000!
A Pennie has said, as you are over 60, the value of the house is not taken into consideration with any financial assessment. If mum had over £23,000 in her own name she would be expected to pay the full cost of her care BUT if she refused, they would still have to provide that care, and then sort it out somehow later.
Is mum currently receiving Attendance Allowance?
Does mum still manage her own money and benefits?
Do you have Power of Attorney?
Are you her DWP “Appointee”?