How Do We Deal with Mother with No Hope of Cooperation?

My 73 year old mother has been gradually showing signs of dementia over the past few years, now it is worse. My two sisters and I are trying to help each other help her. Our story is that after some surgeries and dealing with health problems like MS and UC my mother moved in with one sister but, says she plans to go home even though it has been noted by her physical therapist that she is a fall risk who should not live alone. My mother is still in charge of her own decisions legally and has legal control of her assets, house is paid for, car etc. In other words we can't make a move toward getting her into assited living and she says she can't afford it. Her mental state causes her to make false accusations of theft and imprisonment at the hands of my poor sister who wishes she had not opened her home to our mother. We agreed we would enable her to go home if she asked because she is so hard headed that we feel she is trying to create a situation that will make it look like my sisters fault when she leaves as if she had no choice but, to get out. All she has to do is say "I'm going home" and we will move her stuff and I have told her this. We, of course, don't like the idea of her driving. She will never agree that she is losing her mind and so far any doctor that dosn't say what she wants to hear, never sees her again. Any advice on what steps to take when you have no hope of cooperation from the affected person?