An uncle of mine (in Ireland) had some issues along the same lines. He was hospitalised due to what amounted to emaciation (nibbling cookies, etc, instead of eating actual food) and very unsteady on his legs due to bad hips.
After he was fed to an adequate weight, he needed to leave the hospital and was gung-ho about getting back home. The 'have a rest in a nice Home' persuasion strategy worked eventually in his case, and he's now permanently in a room in a nursing home that he had a voice in choosing. He's fine anywhere he can have his laptop, headphones, and permission to go outside and smoke two cigarettes a day though, and he likes the nurses and the food.
What made a difference with my uncle was the social workers agreeing that he couldn't go home, though in the case of my uncle, his only child is a man, and maybe it was easier therefore to play the 'I've got a job to go to' card in his case - there are all sorts of assumptions made about women and what they are expected to do for relatives whereas the same expectations don't always apply to men. You need to sit the social care people down and tell them there's no way the plan to send her home is sustainable unless they can provide someone to stay with her 24/7. You need to be absolutely firm on this.
My uncle went to a 'Home for a rest' from the hospital and waited there for a bed to become available in one of two permanent homes he had said sounded OK. While waiting, he got used to the routine, food, nursing care, other residents, etc, so it was easier for him to wrap his mind around the idea that the permanent nursing home was his home. You need to get your mum over the hump, so to speak.
Does she have a good relationship with her GP? Any authority figure she trusts who could help to talk her around?