My dad does not want to stay at a rehab facility after hip surgery. Does my father have a right to get up and leave?

Your dad has the " right" to leave. The question is, if he lives alone and falls, fractures something, who will be taking care of him at home?....

Because Medicare might not pay for rehab after an " against medical advice" discharge. Make sure your are protecting YOU.

Tell him absolutely no, he has to finish PT or end up in a nursing home from not regaining function. Sure he can decide to leave and do outpatient PT, but he will not be cleared to drive himself there. Put your foot down.

It must be hard when one feels ok and wants to go home, but feels trapped in a facility for a certain number of days.

One has to be careful about just leaving a rehab before the physical therapist say it is ok to leave. Dad could find out once he is home, he needs more therapy and Medicare might say no because Dad had voluntarily left the facility before being discharged.