She is incorrect, a health care POA does not allow her to make decisions or be the "authority" that everyone has to go through to contact your father. She is confusing it with Guardianship/Conservatorship (although from the sounds of it I wouldn't point her in those directions). A health care directive is a narrow form which only allow the agent to make health care decisions for the other person (your father).
Overall, this sounds like a very ugly situation that's only going to get worse. I strongly recommend you obtain legal counsel familiar with estate planning issues to help enforce your father's rights and your rights.
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I agree with Attorney Majeski. You may need to file for guardianship/conservatorship, if your father is no longer able to handle his own affairs. If that is not the case, and he IS capable of handling things, then you should speak with him about this situation.
The problem you *may* have is that if the police believe you are locked out, then you may be refused access to see your father, unbeknownst to him. An attorney can assist you with this situation, but I agree that this is a big mess, and it may get a good deal messier, before you are through.
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Sorry to hear about the situation. A power of attorney can be as limited or grant as much power as the individual desires. A power of attorney operates even while a person is not incapacitated, thus your sister can legally be making decisions on behalf of your father even if he's currently paying his own bills.
A durable power of attorney would remain in effect if your father became incapacitated whereas a general power of attorney probably would not.
Under the facts you state your sister obtained the agreement immediately after your mom's death, if you have proof this was due to fraud, duress, etc you may be able to challenge the validity of the power of attorney agreement.
You could also file for guardianship, but you may have a strong burden of prove to overcome.
You should probably schedule a consultation with an attorney to go through your facts. Additionally, you should try to get a copy of the POA for the attorney to determine its scope.
The information provided should be considered an opinion only. This information does not establish a client-attorney relationship. Until the facts of your case are completely evaluated the answer provided could change. You should consider setting up a consultation with an attorney in your area.