Is your DH getting any psychological support? Counselling? Therapy? Something like that might help him to think things through more clearly.
Like, it’s unlikely that the HA people are all evil and out to deprive him of his rights. In my experience of social housing management, while I did work with a few little hitlers and nasty bitches, the vast majority of staff were reasonable people trying to do their best.
To be honest, it doesn’t sound as if the housing situation is the main problem. (You say you’d be happy to crack on with an extension, so I’m assuming this has been offered.)
My guess is that your DH is suffering psychologically because of his health problems (my father had a leg amputated (only one, so a big, big difference in mobility from your DH) and looking back I’m sure he had PTSD from all the pain and upheaval).
Would he go for counselling if his consultant or specialist nurse could arrange it?
You have such a range of complex problems to deal with here, OP, and you sound like a really lovely woman. I do feel for you. My mother would do so too, having some understanding of the issues. I hope you don’t have to split up in order to survive but, if you do, come back on here and let us all convince you not to feel guilty.