Actually Jane, I'm not sure we'd simply say "do what's best for your mum". I think most of us would say that you need to find a balance between what's best for your mother and what's best for you and the rest of your family. It does seem a trifle odd that the council are prepared to pay for an extension but not an appropriate stair-lift, but who knows how the minds of budget planners work? Having said that, though, you have to decide if you're going to accept the only thing they seem to be offering: the extension. You know, I don't think it is inevitable that someone with AD will eventually end up in a nursing home. To be brutally honest, at 82, there are a lot of other things that could happen before that becomes necessary. You say your mother has severe arthritis? My mother is now in a nursing home, but that's not primarily because of dementia (she has had several strokes). It is because due to her hip arthritis, she can no longer weight bear, has had several falls due to the arthritis, and is now wheel-chair or bed-bound. If it wasn't for her mobility problems, she would still be living in her extra-care sheltered housing apartment.
Sadly, when you're talking about dementia, confusion comes as part as the package, even confusion about things that are familiar. What I'm trying to say is that yes, moving from an upstairs bedroom to a downstairs one might increase her confusion, but staying in the upstairs one is no guarantee that confusion won't increase anyway.
Jennifer