Should I stay away from my mother who is accusing me of theft?

I moved my mother and father to a lovely assisted living facility a couple of miles from my home 7 years ago. My dad had had a massive stroke and my mother was showing signs of dementia. My dad passed away 3 years later and my mother still lives in the same facility, although a different room. My mother and I are not nor have ever been close. She had a narsistic personality disorder and was abusive to all 3 of us kids growing up. I am 10 years younger than my next brother and seemed to have gotten the worse treatment, which my brothers admit. She recently told me how upset she and dad were when they found out that she was pregnant with me (55 years ago!) For the past 3 years, she refuses to acknowledge my birthday but starts planning parties for my brothers a month before their birthday. Mom is still a VERY difficult person, always waving her fist and calling people names. She is also EXTREMELY hard of hearing, which makes life more miserable for her and for those trying to care for her. My brothers and I all have power of attorney for medical and financial matters. Since I am a retired RN and "the girl" and since she is so nasty to deal with, they have pretty much left everything to me. I visit every 5 to 7 days and usually take her a treat like her favorite soda, popcorn or cookies. I have taken her to doctor appointments, funeral of friends, and shopping trips. Recently, she has begun to accuse me of stealing her car (sold in 2005), her money, and her jewelry (she is wearing it!). She thinks her phone doesn't work (it does but she doesn't remember how to use it) because I didn't pay her bill. She went to the facility administrator and told her that her daughter had stole $57,000 from her and "what are you going to do about it?" I realize that this is all part of her dementia but I have another concern. A couple of weeks ago, she came up with a huge bruise on her upper arm. She couldn't remember how she got but she thinks that she ran into the door. My concern is that she starts accusing me of physical abuse the next time she comes up with a bump or bruise. Is that common with dementia patients? My brothers and my husband have told me to stay away from her entirely, which may be just what she wants. ?? Any thoughts would be greatly appreciated. I'm thinking that no one cares!