How would moving her to a retirement home help? All prevention is what to do after the fall, i.e., call 911. She doesn't use her walker at home consistently, doesn't carry the cordless phone or cell at all times, gets in shower when alone even though we have someone who can be there. I work full time and my home has stairs, one bath upstairs, etc., dogs. If I move her to a retirement community how will they keep her from falling in the hall while talking to someone?
Her doctor was getting frustrated with her falling, going to the hospital then having him send her to rehab. If they won't help themselves, then the staff at the facility will make sure they do; at least in a nursing home, from my experience. This being stubborn mentality gets old especially when we have to pick up the pieces constantly from their bad decisions which are based on non-compliance to doctors orders. My mother eventually suffered a blood clot on her brain from all the falls, which she miraculously recovered from, only to go back home and not follow doctors orders. There is only so much you can do.
You say she is acting child=like so this probably is indicative of dementia starting. I would start researching and visiting facilities and then talk to your mother about it. My mother is in a lovely facility with plenty of activities and entertainment, etc. If you need more info, I would be happy to provide it to you.
Good luck and blessings to you and take care.