I assume you are over the age of eighteen?
As far as I know, as your dad is still alive (so technically the closest next of kin) but incapable of making a decision, you may need to apply to the court to get the legal right to make decisions...talk to a solicitor to get full clarification. Or even have a brief chat to the doctor/nurse whose care she is under as they should have certain checks they need to make if there is a query about the next of kin (obviously it won;t be legal advice, but I'm sure this sort of thing crops up alot).
Also, go easy on you aunt....you may also need her supprt in the forthcoming months, she probably just misunderstands as she was next of kin for her other sisters.