Years ago my role within the Local
authority was to assess and fight for people exactly like your partner.
I'm sure you would have been given this information, but just in case it's been missed, and is still available, this is what you should have in place;
A competent top tier Occupational Therapist Care Manager funded by Social services. They would come under Adult Services. They are dual trained for mental health and physical health.
This person can liaise with social workers and the mental health teams to give you the ongoing support you all need. This is a difficult challenging situation requiring substantial input.
You need a carers assessment.
The OT can fight your case with the council to get funding. It might be that you have a case for a sizeable downstairs extension with wet room and facilities and an internal lift to enable your partner to look after his children. It might be this particular house is unsuitable and this adaptation could happen on another property.
I'm hoping this is all still in place, it's been decades now since I was in this role. I know of families in the past in similar circumstances to you and with help, funding and support it worked.
I understand your logic totally, the way poor mental health affects relationships is crippling.
Do what you need to, it may be leaving is now the option you need most rapidly to stop your mental health from deteriorating further. But meet with the Team Leader of the Adult Services Team before you decide.