This question has been asked and answered before. If you are having problems getting them released to your care you need to get an Ombudsman involved or a lawyer. We can suggest but you have to follow thru.
Do you mean go out for lunch, overnight, a few days for the holidays or move away? Bear in mind a doctor had to sign medical orders that they needed 24 hr medical oversight for them to get in. If they are private pay, they may have more flexibility. If they are on Medicaid there are limitations to how long they can be gone. You would need to check with the NH for what is acceptable.
https://www.agingcare.com/questions/parents-are-in-nursing-home-can-a-staff-member-deny-me-to-take-them-from-the-facility-if-i-have-poa-454360.htm
Bear in mind a doctor had to sign medical orders that they needed 24 hr medical oversight for them to get in.
If they are private pay, they may have more flexibility. If they are on Medicaid there are limitations to how long they can be gone. You would need to check with the NH for what is acceptable.