Re: Home care or rehab facility?
This is sort of a hybrid answer: I would research rehab facilities nearby and get the pre-approval from your insurance. That way, if you feel like you need to go to a rehab facility, you have everything in place to do so.
In addition, if the hospital discharges you because you are medically stable but won't allow you to go home, you can research a facility ahead of time. My roommate in the hospital had her hip replaced. She was medically stable, but could not ambulate on her own. Thus, the hospital could not keep her for a fourth night, but she could not go home either. She and her husband were stressed and scrambling to pick a rehab facility. Not sure what she did about insurance.
(I'm a planner, so having options available makes me feel more secure.)