My brother had power of attorney over my mom in the end. He put his granddaughter in the house for a while. Until the neighbors were calling him every day complaining about the dog poop smell coming from the house, then he told her the house had to be sold and she had to find another place.
So he cleaned it up and sold it. My sister and I never saw a single penny of it.
Power of attorney means she can do anything she wants and YOU have zero input. One of my friends went through this when her mom suddenly passed away. "She" was the executor of her mom's will and was even living with her mom when she passed away. Her brothers lived far away and had hardly anything to do with them.
Her mom has been gone about 12 years now and everything the woman owned is STILL in storage because the brothers both contested the will and wanted everything for themselves. The sister pays that storage bill every single month and every penny of the cash mom had has gone to pay for this and now she's paying the charges out of her own pocket. She lives off disability and only gets a few hundred per month to live on. It's a large storage, bigger than a garage and it cost something like $100 per month.
Her brothers are specifically fighting between themselves over some old bottles, seriously, bottles their parents had sitting in windows and on shelves. There isn't anything my friend can do either, they've gone to court numerous times. One of the brothers married an attorney and she keeps everything tied up year after year. I think they're hoping my friend dies and then they can take everything.
If this isn't something you like then you need to legally address this if she isn't willing to allow you to have any input.
I'd say what's done is done. If you are interested you could buy the house for your half. You find out the value of the home then figure out what is owed on it. Then discuss an offer with an attorney and buy the house, you are basically giving her what a sale would bring in for her inheritance. Or if the parents are expected to live many years you could lease purchase it where the money you pay each month goes to her and she pays the mortgage or uses it to pay for their care. You could even just buy it through a bank and then rent it out to someone. Surely you have a good friend that still lives near the homestead who could oversee the showing the home to a potential renter and take calls for repairs if needed? Maybe they know someone who could rent it too.
She really doesn't need to pay for things out of pocket. They must have insurance or medicare or something to pay their bills. If they have no house or anything in their name their insurance will have to pay for much of their care. She could get a home health aid to come in at some point to help with their physical care such as bathing and things. There are many resources she can get for them that their insurance can cover.
I feel bad for your parents. And your sister for having to take this on. It's hard hard work. Taking care of elderly parents who are suffering from mental health issues like dementia is depressing and continually reminds a person of what they might be like in 10, 15, 20 years.
I hope the 2 of you are on the same page about this. It will make your life much easier.