This is a difficult situation that depends in large part on how the facility is classified. Depending on the classification and your state’s laws, the facility may have to go through an eviction proceeding just as if your father were living in an apartment. This can take time and give you and your mother time to find an alternate living arrangement for your father. It may also be classified as a health care facility with its own procedures.
A local elder law or legal services attorney should be able to advise you. Find a qualified elder law attorney near you. There also may be a senior or residents rights organization in your community or an ombudsperson service that could help.