You sound like a very caring and loving son and I can understand why you want to look after your mum but I will echo the caution of a couple of other posters.
A friend’s mother went into a care home because of her dementia, her dad still lives in the family home. Her mother lived for 9 years in the home until she died. My friend would visit her mum and dad twice a week, doing all the practical stuff for her dad at home, then onto the care home to visit her mum. The journey is 90 minutes each way. Her dad now has Alzheimer’s she is his main carer, with paid carers going in every day to give him his lunch. He has recently become incontinent and so when she makes her visits twice a week she is having to shower him and clean him up. This has caused huge distress to them both.
Her dad is constantly moaning that he’s lonely and she is at his beck and call. He won’t move out of his house and keeps on telling her how much he appreciates her. That’s fine, but her marriage has suffered, her mental health has suffered and she can see no end to it. She’s 58, her dad is 90 and I can see him outliving her.
Her brother who lived nearby met a new partner and has moved 150 miles away. You do not know what lies in the future for your sister, she may end up not being around as much as you originally thought, she may lose interest, who knows. You may move back and find a new partner and can’t take them home because mum becomes jealous of someone taking you away from her. Just think about whether you want to live with your mum really carefully.