This is a difficult and not unusual situation. The Medicare payment structure provides incentives for hospitals to discharge patients as soon as safely possible. The hospitals then put pressure on patients and their families to accept discharges to places that may not be optimal. Fortunately, there are some ways to delay hospital discharges, even if by a few days, which could give you more time to advocate for the inpatient rehab. The hospital may give your father a notice of non-coverage saying that Medicare will end if he does not move out. The first thing to know is that he can stay until he receives this written notice. Second, he can appeal it. The notice itself describes the method for doing so. Making the appeal should get him a couple more days of Medicare coverage in the hospital.
For more information about fighting a hospital discharge, click here.
For more information about appealing a Medicare decision, click here.
The Center for Medicare Advocacy has a lot of information on its website about how to enforce Medicare rights: https://www.medicareadvocacy.org/