Catch-22: Mom needs rehab but did not have a recent hospital stay. What are my options to get her into rehab?

Mom has had so many things happen recently that required trips to the ER, tests, visits to her doc., etc. This has left her weak and in pain from a shoulder injury. She lives independently and if she does not get her strength and mobility back, I fear that she will not be able to live as she wishes. The rehab centers say that she needs a 3-night hospital stay before she is elligible for Medicare rehab. She could probably get an in-home PT but she still could not be alone all day. We can manage some in-home care for her, but cannot do this all day, every day until she heals.
If you have dealt with a similar issue recently, I would appreciate your input. What do I do if she cannot be in her home for now?
thanks,
Lilli