From what you describe, it doesn't sound as though your mum is particularly difficult! (You may think differently...!)
Most homes can cope with all the things you mention, as long as they know that's how it will be. But help with mobility and showering is pretty much par for the course. Ditto incontinence - I don't know if she is...
The sort of things they struggle with are: unpredictable behaviour, maybe violent or aggressive, particularly if the person is likely to bother the other residents. Resistance to personal care. Again, violence of any sort obviously makes personal care very difficult. Other factors might be considerable nursing needs though it doesn't sound like that's an issue. (Not all homes have a nurse present. A place that calls itself a nursing home does - they will have a nurse on the premises 24/7.)
Other things to ask might be funding. Ask the home what would happen once your mum runs out of money. Some places will accept the LA rate (much less than most self-funders pay) if a person has been resident in the home for a couple of years +, paying the full whack. Others won't. Once SS start contributing to her funding, they will dictate (pretty much) where she stays and they may want to move her to a cheaper place that will accept their rate. But that's in the future, and who knows what the future holds...?
Hope that helps a bit!