I think my mother (85) has early onset dementia, but hasn't been officially diagnosed yet. Should she stay in AL or go home?

In April, she had a UTI, which as common w/seniors, but she had a horrible reaction to it. She had also called twice in as many days. She went to the hospital after it took 6 firefighters to get her out of her house! Then she spent months in a nursing home. We eventually got her a place in an AL place that also has a memory care area. She hates it, argues w/the staff & wants to return home.
There are times she isn't lucid & comes up with crazy statements and she doesn't have a UTI! She will be lucid, say something crazy and then lucid or be lucid for entire days. She is incontinent and refuses to have staff change her, wash her or do her laundry as she states they have stolen her clothes when they do her wash. She says by her washing/showering herself, it shows she's stronger so she can go home.
A part of me thinks she can go home but another part feels she can't even tho she is lucid a lot now. Also, I know she feels like she's a prisoner being held against her will now. No, she can't live w/me as she was horrible to me growing up w/a lot of mental abuse. She's lucky I have a conscience and am making sure she's cared for with what she did to me.
She has made me POA & executor of her will (which is everything for my garbage sister who she adores & no she can't take care of my mother). But she sometimes thinks I'm stealing from her (I am not but I am paying her bills). Getting money to keep in our account from where I pay her bills from is a fight! Everything is a fight with her...& I understand no one wants to give up their independence. Idk how much is that vs possible dementia.
Should she go home? Oh and she also doesn't eat nor drink as she should & hoards food both in her house & in the facility!
Hiring someone to stay w/her @ her home is too expensive and she would need someone I think 24/7 or close to it, so that's out of the question.