It depends on whether your father is competent and has also granted authority to the girlfriend. If not, you and your brother may insist that the care provider follow your instructions.
If there is a joint bank account with the girlfriend, she will have access to those funds as long as the funds go into that account.
This can only be a partial answer, as I do not know all the particulars of your situation. If there is a conflict with the girlfriend, I would recommend you invest in a few hours of an attorney's time to determine what actions, if any, you should take for your father.
Good luck.
