Joint POA's disagree about father's care.

Joint POA...This is the biggest obstacle when you do not agree. The wording on the papers are very important. Are you sure it is joint? If the bank accepts one signature, the facility and whatever else you need to do, you may have a shot otherwise you may need to seek a different way, guardianship or let the court decide. If I were you I would try to talk to your sister and explain to her that it is her fiduciary duty to see that your dad's best interest is the power your given not her best interest. Google fiduciary duty and let her read it. If she is not doing whats best as her principals (your dad) interest you got a case.

Joint POA sucks.

No, that why joint power of attorney's are not recommended. Best to have an agent and an alternate. Sorry, unless I am wrong, I believe you and your sister need to come to an agreement or get your father to appoint you power of attorney if he is capable. That will probably not go over well with the sister. Good luck to you.