How do I deal with my mother's animosity towards me?

My mother has vascular dementia, has lost her license and depends on me for grocery shopping, scheduling doctor's appointment's and interpreting their comments, ordering and giving her her medications, making sure her dogs have meds, calling repair men...use to do her bills but she has accused me of stealing from her. She's told everyone she talks to friends, neighbors, other family members, her cleaner. She got her neighbor to get her into her accounts and the institution determined that I had not been stealing, nothing had been taken out of the account. But she is still accusing me. She has not gone back to anyone and told them that I actually had not been stealing. That same neighbor gave her her Humira injection and I almost gave her another one the same day. I happened to see the used pen on the counter just before I gave her the shot. She blames me for losing her license and not getting it back for her. I spent one year setting up tests neurologist, GP and driving school. She did not past any of the tests, not even close, including cognitive function exam. That was two years ago. I have not stolen from her. I do her paperwork for her. She sat at the table with me while I paid her property taxes online, gave her the receipt and she still accuses me of stealing the money. I've taken care of her for the past 3 years and the previous 4 years I took care of her and her then boyfriend who was in a wheelchair from a stroke. And it goes on and on.

I've hired caregivers to come in and help--but she either runs them off or won't let them in. She did let one come in but would not pay her. I had to pay her. My sister and I both have tried to get her to go into a residential facility but she refuses.

My mother told me that I don't do much for her. I can't do anymore and I'm thinking about doing less. My sister lives 3 hours away so I do everything.

I'm so tired and unhappy.