My PWD has all the signs of Alzheimer's -- official dx is scheduled in September -- but she also has oddly lucid moments that sometimes don't correspond to reality. I can't provide all the things she needs help with -- lately I can barely take care of myself due to exhaustion. Can the facility override my orders of "unsafe to discharge at home"and disposition not tohome? I need to know that she is there permanently, so I can rest and take care of my health again.
Why would you want to keep POA though? It really sounds like it's not worth it. If I were you I would not take this person out of LTC. If you can't take care of her yourself (and its going to get worse) and there aren't resources to have 24 hour caregivers, leave her in LTC. That does not mean that you have to give over POA to the LTC facility though. You can still administer her finances and her medical decisions.
You need to concentrate on your health and well being.
If there are other family members that can step in if she is legally able to appoint someone else as POA that can be done. If a lawyer or judge does not think she is cognizant then the Court will appoint a Guardian. (If there is a family member willing to be appointed Guardian that will happen as Court generally wants a family member or friend to be a Guardian rather than a Court appointed one.)
If your aunt has the funds a "respite" stay can be arranged if they plan on discharging her. The respite cost would be paid for by your aunt NOT you.
But given your health condition I would contact the attorney that drew up the original POA paperwork ASAP and notify them that you have to step away from your POA status.