What happens to my dad's POA document once he is diagnosed w/ Alzheimer's and designated not capable of making decisions?

I am my father's POA, don't live in the state where he lives, and am concerned because he has several children from a different marriage who are after his assets. He has just been diagnosed with dementia and probable Alzheimer's. The last time they came to visit (I was not present) and they took him to the bank as soon as I was off on another errand. They claimed I was keeping his bank statements from him and refused to listen to me when I told them that he sees his statements when he asks, but doesn't remember. They even called Adult Protective Services on me even though I have been the sole person who turned my life around to care for him after his wife, my stepmother, died this summer.
I have to leave to go back home, but my question is what happens when someone is medically designated incapable of making good financial decisions--does their POA take over, or what? Was considering guardianship but my attorney said I should not go for guardianship since I am already his POA. Would love some info on this! Given his vulnerability I am concerned about him being protected when I am not physically present.