Can my father appoint one daughter POA and one his guardian/ caregiver?

It really depends on your family dynamics, if you are all able to work together then everything should be fine but when there are disagreements there can be trouble, especially if the two with all the power work together and leave you out of the process. As caregiver you are the one who will understand your father's needs best and only you can determine your physical, mental and financial ability to continue meeting them, I personally would not have liked having someone else in control.

Yes.

Even if your father gives (health care/medical) power of attorney to your doctor-sister, she will have responsibility only for making decisions about his care: she will not be responsible for carrying it out in person. The decisions she makes must be in his best interests, but they must ALSO be in line with his known wishes as far as is practicable.

So if your father has made it known that his choice is to live with you and have his care managed by you, and there are no concerns about your ability to meet his needs, your sister should comply with that previously stated choice.

Having said that, if your sister has reservations about the arrangement and believes that your father would do better in a group home, you would be well advised to listen to her reasons. What are they, have you discussed them with her?

I would not become a caregiver unless I had POA.

Are you proposing to care for you father 24/7 without any help? Without respite?

If you need to hire help, will sister with POA release funds for that? Will she see the need for you to have regular respite? Will dad accept that there will need to be non- family helpers hired to assist with his care?

As your father's dementia worsens, he will almost certainly need to be in a facility. If enters a facility while he is still somewhat cognizant of his surroundings, he may be able to make a better adjustment.

You would have to pursue it through the courts and may require the services of an attorney.

Who is currently caring for him? Why do you want to care for him "by us"? Is there no way to improve the communication with the medical PoA sister? What is the problem?