You can call the rehab hospital. Ask if there is a patient advocate (or similar) on staff. If not, or if they are not able to help your situation, then call your dad's surgeon's office - presumably, the surgeon is the one who recommended him to the rehab hospital.
If there is no one at the rehab hospital to talk to, and no one at the surgeons office will respond (ask to speak to the surgeons nurse or PA (physician's assistant) or an insurance coordinator) then you can also call the insurance company that covers your dad's care, and talk to them. Don't be surprised if any or all of them tell you that your dad really needs to stay, and complete his course of care.
It's VERY important to remember that unless your dad gave them specific instructions about talking to you, or your mom, that these people may not be allowed to discuss the specifics of his care or condition with you. That's because of laws governing the privacy of patients and their medical information.
In the meantime, you can help by reminding your dad that the sooner he participates in his physical therapy, the sooner he can go home. It sounds like one (or more) of his doctors is/are concerned that if he goes straight home, he could have a less-than-desired outcome without direct intervention from the rehab hospital. In other words, if he goes home now, it could mess up everything that the surgery tried to fix.
There may be other facilities that he could be moved to, and stay at; Rehab hospitals are often favored by a patient's insurance because they typically have a lower cost per day. They are favored by doctors because patients continue to receive a higher level of care than they might in an outpatient situation (at home). Your family needs to consult with the surgeon first, before moving him - there may be a very specific reason why your dad is at that particular rehab hospital. (like they have someone on staff who works with people who have had foot surgery specifically)
But honestly, the fastest way out of this is for your dad to be a big boy, and do his physical therapy, cooperate with the nurses and doctors, and show them that he is ready to go home and be self-sufficient. He also should be aware that even once he is home, he might have visits from Home Health (or a similar service) that will come to check on his progress at home, and can even administer physical therapy at home. Additionally, he will quite possibly have outpatient physical therapy once he is home, where he will go to a PT center or office anywhere from 1 to 3 times a week, for about an hour at a time.
No one likes being in the hospital; you are not in your own home, your own comfortable surroundings. There are people telling you what you can and can't eat, you often can't wear your own clothes, you don't have any say in your schedule, your meals or often even when you can shower and do other self-care. But it's not meant to be a vacation - when someone is in the hospital (whether it is a "regular" or a "rehab" hospital) it's because they need direct medical care by experienced professionals.
You can help your dad the most by encouraging him to keep working with the hospital staff where he is. I know that you and your mom miss him, and want him home; that is very evident. But your focus right now should be helping your dad get better, not trying to bring him home before his treatment is complete, or before he is medically ready. Be cheerful and supportive; bring him books or magazines, or even an iPad, a GameBoy or a Switch, or some other things that he can help pass the time with. Encourage him to be interested and involved in his own care, and keep the focus - for him, your mom, and you - on his recovery.
You can also try to politely work with the nursing and administrative staff at the rehab hospital, and explain some of your family's (and your dad's) concerns to them. They may have some solutions that could help your entire family be more comfortable. They can't fix something if you don't tell them about why it is a problem.
Your dad has already gotten over a couple of major hurdles. He had the surgery, and now he is healthy enough to be transferred to a rehab hospital. That's really good news. The fastest way to get him home from this point is to be focused on helping him do whatever he is supposed to do to get well enough to come home.
