What a rotten situation you all find yourselves in, Leswi.
Your poor dad: his heart is giving him one set of messages, yet his body and probably his mind, badly need a rest, so he's utterly torn. He probably does realise that practically your mum is in the best place for now, but after so many years together, he can't bring himself to accept the separation. He may feel he's letting her down, too. And getting upset is not helping his own health.
However, this is a pattern that does not appear to end well - if your mum goes home, he can't really cope and the respite will be needed again, but he'll back out, take her home and round it goes again until a very real crisis.
Personally. I'd be trying every excuse under the sun to keep your mum in respite 'just another day or so' every day, so that he has a 'reason' to let things be that day - and the next ....
You know your parents best - will he respond to you (or an authority figure eg GP, consultant) sitting him down and laying it on the line? He may be wanting someone to do that for him so he can be 'forced' into accepting the situation rather than having to make the decision. Will he take you into account - often dad's will do things for their children's sakes - if you lay it on how you are feeling and that you are so worried about them both ...? Will he respond to practical 'solutions' so that you make sure he can visit whenever he likes and joins in activities ...? Or does he need to be told some 'tough love' to let her stay and stay away himself or both of them will become too ill to stay together?
It's a horrible situation for him, as a husband of long standing, to face being separated from his wife - maybe he needs to talk that through, and if not with you, is there someone he is close to, or his GP, or can the home manager have a tea and chat session with him?
If he insists on having your mum home again, are you in any position to gainsay him legally? Would you do that even if you can - or hold off for later?
Are you able to at least negotiate with him - mum comes home AND to make sure she's supported (and you have some peace of mind) he agrees to as many carer visits as possible, a cleaner, some day care (so that both get used to being away from each other and dad gets used to not doing all the physical care tasks) and a night carer (would he agree to separate rooms so that he is not disturbed when the carer is helping your mum - put it to him that separate rooms in the same house is 'better' than separate homes), and any other support eg alterations to the house; grab rails etc.
I appreciate all this depends on their financial positions and lots of variables only your family know about.
Just some thoughts - feel free to ignore if not at all appropriate.
I really hope you all find a safe resolution to all this.