I am not sure why the caregiver is meddling here. However, as long as your parents are competent, you do not have to comply with the caregiver's directives. You are under no legal obligation to even listen to him if he is not the Durable POA. His wife cannot delegate the DPOA to him.
As for demanding that you buy your sister out by mortgaging your parent's house, that would be considered elder financial abuse. So, you should not do that.
Finally, if you object to the expenses on caregivers, you need to let your parents know your thoughts. The expenses can be cut. Again, if your parents can still speak for themselves, they can say what they want regardless of who has Durable POA. Durable POA does not mean that they cannot speak for themselves. It just means that they have appointed someone to also act on their behalf. However, if they object to the actions about to be taken by the DPOA, the DPOA must comply with their wishes and not override them. The DPOA is an agent of the Principals and must comply with the Principals' directions. Otherwise, the DPOA would be breaching her fiduciary duty.
A 5-star rating to my response is appreciated so that I can receive proper credit for responding to your post. Kindly use the popup screen to give the rating. There is no additional cost to you for giving a 5-star rating.
Thank you for your cooperation.