What are the rights of the caregiver?

Joekool
Your question…what are the rights of the caregiver?
Your rights are absolute if you choose to walk away. Or as far as your emotional attachments and legal documents will allow you to go.
Home health is good but hospice provides more unless your uncle wants blood tests and other procedures with intentions to extend life to be paid for by his medical insurance. Even then, he can go off and on hospice. There is no requirement to stay on hospice. It is meant for the comfort of the patient.
Why does he prefer home health to hospice? I asked for hospice for my DH aunt when she became incontinent. She could get more baths with hospice so I switched services for her.
Do you have your uncle and aunts DPOA? Do they have children?

You can but if you do not have POA the doctor may not be comfortable discussing his care with you. I am just wondering how this would even solve the issue. If the only bathroom is upstairs and he can absolutely not manage them then I think an option would be one of those electric chairs. I don't understand the hospice issue for both of them. Perhaps you could provide some more specific information regarding the actual health issues each of them are facing beyond the staircase one.

You can definitely call his doctor with questions/concerns as to why hospice was recommended and home health apparently was not. Are you sure the doctor has permission to talk to you? I'd start there.