Hi OP,
Be totally hardline about the care that must be in place before he comes home - often this goes against the grain but your strongest negotiating position will be while your DF is in hospital not at home. Push for adequate length of carer visits, e.g. to bath him. push back when they want to make short cuts e.g. they can have a flannel wash and not a bath, ask they whether they would be happy for that level of care for them or their parents. Make sure all the equipment, hoists, commodes etc. are in place - you should be able to get an Occupational Therapist to visit to ensure work is done before he comes home.
My experience with one relative was a few days after discharge they persuaded their elderly partner to drop the lunchtime visit so tell your mum not to agree to cutting visits, at least not without your involvement.
I’m not an expert with all the the benefits but I did complete the forms for Attendance Allowance. I also believe they may benefit from. Council Tax discount if you can argue they need extra space, e.g a bedroom for your dad.
My MIL has great carers that she considers friends, but we arranged them privately - the LA pushed back initially and she has to pay a bit more herself than to use their carers. Another relative had very poor carers and their next of kin had to install a Ring doorbell to monitor the length of the visits. On the financial side, they will go through everything with a fine tooth comb, when my MIL went below the savings limit her LA kept checking things like the buggy insurance from a year previous etc. - hardly deprivation of assets.
Keep notes of who you speak to, full name and job title and what is agreed and any review dates, e.g length of visits, how many visits per day, what the carers will do etc. and the fact there will be no financial contribution from your DF for the first six weeks.
I don’t think they can force them to sell the house but get expert advice.
Also, I believe your mum will be entitled to a carers assessment so her needs are properly considered.
Good luck and sorry to sound so combative, I have had some very challenging conversations with people who should know better (not the carers who have been very caring and skilled).
Do you have Lasting Power of Attorney?