My mum has late stage Alzheimer's and although she lives with me, she has carers 3 times a day for her personal care, they wash and change her etc as she is unable to leave the bed. She no longer moves and has a hospital bed with an air mattress which moves her about to stop her getting pressure sores. She does have one of those baby toys which is a soft animal with different bits to rustle, chew on, rotate, rattle etc and I put the radio or tv on for her. With Alzheimer's the brain gradually loses all ability to do anything and so she can do no more now than a three month old baby. She can no longer chew and so lives on food replacement milk shakes.
I have spoken to her carers and they provide a full range of services for their clients who can be of any age and with any disability. They provide 24 hours care for clients in their own home with carers rotating round the clock. So if you and your mum are happy with her current carers ask the company what they can do and how much it would cost her. If 24 hour care is the same price as a residential facility she could stay at home depending on the type of dementia.
You hear such terrible stories about residential care that I'm happy with my mum taking up my lounge until she eventually goes. She's 89 and has been virtually immobile for a year now but is physically quite fit as she's not on any medication, just her brain closing down. Although mum has to pay half of the cost of her carers with the council picking up the rest, all equipment is loaned free of charge. When she still showed an interest in her surroundings she had a specially built chair that held her upright which she was hoisted into for a few hours each day. Her pads are free, as are the various skin cleansers and skin protection creams she needs, even her special milkshakes are free on prescription.
Sorry I've had a bit of a ramble too but what I'm trying to say is that home care is possible depending on the type of dementia. As I believe that with some dementias the patients stay mobile which could be more of a problem. Anyway you are doing your best for your mum and that is what counts.