What do I do when my mother with dementia accuses me of taking her credit card and threatens to throw me out of the house?

My mother has early onset dementia. If you didn't know her you wouldn't be able to tell that anything is wrong until she started to talk like a truck driver. She is very manipulative and super mean. This is not the mother I grew up with. She went to her doctor saying I threaten to hurt her if she doesnt let me use her car. He called the police. Also I have lived with her in the family home for many years. I pay all of the bills and buy the food. I do all of the cleaning and cooking but she still yells at me and threatened to have me evicted. I don't know what to do. I feel like the bottom has dropped out of my whole world. I want to leave but I fear my greedy sisters will run in and take all she has left. They have stolen from her before and are being nice to her now after not speaking to her for over 15 yrs. Help where do I turn?