Are there places available for an elderly caregiver/ spouse to get rest and personal rehabilitation?

Agree with funkygrandma. Might be time for hubby to be placed permanently. She needs to take care of herself first.

Perhaps it's time instead to be looking into placing her spouse in the appropriate facility once he gets out of the short term facility. There should be social workers at the short term facility to help her find the right place for him.
Anyone that is in "dire need to rest and recuperate," needs to be taking care of herself first, or she will be the one dying before her husband.
Here's hoping that you can talk some sense in her, before it's too late. Good luck.