Perhaps you could try telling her that she needs to prove to you and her family that there isn't anything wrong with her and in order to prove this,she needs to go to the dr and have tests (non painful tests).
Once the dr does say the inevitable (spelled) then tell her what I told my father on more than one occassion when he realized he didn't understand why he was doing things..I told him it was his disease and he couldn't help it

Find the cleaning guy and and make a talk. Or call social services, if she is not capable talking care of herself it's the best that she is institutionalized. I am from different country, but suggest that you look what are legal obligations towards old people - how much can you help her, but not brake her legal rights.

Thanks for the advice. She gets very angry when we imply that she's forgetting things or that her stories are very unlikely. I'm not sure whether or not she's fit to live alone as I don't see her often. I do know that fit or not, she's headed in the wrong direction.

We are going to reach out to social services for advice to see what they think should be done at this stage.

My mom became very combative at a point and I had her doctor put her on the anti psychotic Haldol that is sometimes used for Alzheimer's

There were some not great side effects however it really did make a positive difference in moods and behaviour.... big hug.......xo

I have a step-mother-in-law (Mary) that has Alzheimer's and Dementia, her short term memory is gone, which results in the same questions over and over. I have worked with some councilors and they have told me simple, brief answers. You wont be able to convince her about the cleaning guy isn't breaking in, once they have a story set in their mind, it stays. Its a part of the disease. Best advice is to redirect her.
Mary had it set in her mind that my boys were going over to her house, sleeping in her bed and watching her TV when they were out of town. This has gone on for 5 years now. The last time she brought it up, I told her how they went off to college and they lived in a different town. I did not deny it, just told her where they were. She realized it couldn't be them, now she believes the house is haunted and she has a ghost sleeping in her beds.
We did finally move her into an assisted living facility awaiting an opening in memory care.
We have been lucky, both sets of parents have freely given us their important legal papers. You might have to be creative in trying to get a copy of them, perhaps talk to her attorney.
Good luck to you!

It's so heartbreaking to watch a loved one go through this. It's been almost 8 years that we've been caring for my mom. It all started after my dad passed suddenly and Mom was alone in her home. She would call my sister to tell her that there were people tunneling into her basement, men singing all night keeping her awake, little girls coming into her room and messing with her stuff... on and on. We had no idea anything had been going on with her, Dad kept it all to himself and so these hallucinations she was having were shocking to us. Once she moved in with me and was taking her medication reliably the hallucinations and delusions were minimalized but those "loops" that she would get into - "Where's Mom?" "I need to go home", "When am I going home?" over and over and over through the day, shadowing me all over the house. I thought I was going to scream sometimes. It will begin to diminish. I found that trying to reason with her, to try to dispute what she was saying only made her more agitated so we had to find ways to pacify her. You could try telling her that the police are looking into her case, maybe try installing one of those fake "video cameras" so she feels more secure? As far as the POA issue, first and foremost, does anyone know where she keeps these papers? it may be that you'll have to ride it out for a while until the disease progresses and she reaches the point where she isn't really cognizant of what's going on. Good luck!