Well yes it is confusing. And I'm probably going to confuse you further as I have a number of questions, to which you may not know the answers
. As I see you have a number of issues here. For a start, when your father was admitted to the hospital, was he sectioned? Was this move made after a request from the home? How long ago did this happen? Is it likely (or even possible) that he would return to this home? What sort of contract did your mother sign with the home (this is the big one because care home contracts often require you to give a months notice).
Your mother's savings aren't relevant when it comes to paying for care: only your father's and 50% of any joint savings.
Sorry as I say - a lot of questions.
Honestly, if the care home decided they were no longer willing to care for him and will not be able to do this (or you simply don't want him there any more) I would clear the room and give them notice. TBH, few care homes offer a discounted rate when their residents are in hospital (in part because apart from food, they still have to have the same number of carers on duty, run the laundry etc so unless a major portion of the residents are in hospital, they have essentially the same overheads). The one issue you might have with this is if the hospital suddenly decides he can be discharged back to this home, then he has nowhere to go, and if you require any form of LA financial support they might be sticky about it. Of course if he was sectioned (under a section 3) he will, on discharge be eligible for 117 aftercare (which essentially means that the NHS and/or the LA will then be paying for care).
If he has been sectioned then I can strongly recommend the mind sight (mind.org.uk). They have some very clear information about what sectioning is and the ramifications of the different types.
Again, sorry for all the questions.