The other thing to remember is that making major life decisions, such as moving, are not best done in a hospital setting.
Unless she has had a major change in function, such as a massive stroke, she needs to go home - perhaps with a care package - and then make a considered decision.
I visit residential care homes as part of my job and, from what you say,, your mum really won't fit the profile of one. If she's wanting company etc then sheltered housing or Extra Care housing would potentially be much more suitable for her.
In a care home she would only have one room, and many people she would be living with will have cognition issues. Of she's got reasonable mobility and cognition then a care home will not be the best place for her.
My 91 yr old MIL broke her arm last year and, when discharged from hospital, was sent to a care home for rehab. She spent the first two weeks saying how wonderful it was,and how she wanted to stay there forever. She then spent the next 2 weeks demanding to go home as the novelty had worn off and she was desperate to have her own space and independence.