Over here they look at anything of value that was sold or given away in the past two years, as a lot of people were signing their houses, etc. over to relatives. I guess you will find out if she qualifies or not. If there's a number you can call to ask about financial eligibility (or a web site you can find), without giving out information about your mum, maybe you can find out something that way.
They all seem kind of clueless, don't they? Well, of course her mobility is poor or non-existent--she has fallen so many times she has undoubtedly done damage to the hip replacement. Do they need an order from the ortho surgeon to do a simple x-ray?
Unfortunately, I think you are right: They will get her to a point where they feel comfortable in discharging her home and it will be the same old, same old again. Who knows how long this could go on?
You take care of YOU--that's of utmost importance.