The question you need to ask yourself, is
"Should dad's move from the rehab home be his final move, to somewhere his needs can be catered for 24/7 for the rest of his life?"
His dementia and physical health are NEVER going to get better long term. Imagine a graph, it will go up a bit and down a bit, but the ups will never be quite as up as they were previously, and the downs will only get deeper.
I know this is hard to accept, but what is in dad's BEST INTERESTS?
Is it better to send him home again, to fail again?
How long before you go round this awful circle of admission, rehab, discharge, admission....again?
Believe me, I know how tough it is, all four parents have now died, each after a long illness and many admissions.