My mother needs to go to rehab for physical therapy but she's too stubborn and wants to go home. What can we do?

Just make it clear to discharge that YOU are not taking her "home to an unsafe environment where there is no one to care for her". Just keep repeating those words.

Also, "mom, you were SO smart to check yourself into the hospital when you realized that something was wrong! I'm so glad that your medical team has a plan of care for you, which is to go to a rehabilitation place to get strong enough to return home; I can't imagine that SOME people would be foolish enough to turn down an opportunity like this to get stronger, and Medicare will pay for it".

Barb is spot-on with her answer. Don't take Mom home and don't provide a way for her to get there. Talk to social services at the hospital and make it ABUNDANTLY clear that you cannot care for her at home, that it is not safe for her to be there, and that she needs rehab. They will know what to do.