Oh dear, it sounds like you are right to be concerned about the doctor she has found for him. And about the demands being placed on you.

He and his daughter don't have the right to force the entire burden of his care onto you, nor to be at his beck and call every minute. Buy him a "reacher" and put it by his recliner or on his walker so he can pick up after himself.

My first question is, what would he do if you just hired help to come in and clean without his "permission"?

And to settle the daughter issue, just tell him when you are going out, and that if he does not want to be alone, he can call his daughter or a friend to stay with him. Leave what he needs within reach and go. Probably not for a week (which is what you really need) but for a few hours. Then go.

Finally, have you visited our caregiver support group to connect with others going through the same issues as you? https://connect.mayoclinic.org/group/caregivers/

Sue