I'm sorry you're going through this. My sister-in-law faced similar circumstances last year, although her husband passed away unexpectedly only a couple of months after becoming disabled.
She did daycare, which let her care for him at home, but I don't know how she managed it. Her DH couldn't feed himself or manage his own hygiene.
Have you considered one of those companies that buys homes? I've seen them advertised, I don't know if they are legitimate or would give you a fair price. But in truly desperate circumstances, it might be worth it to have the house not listed as an asset when it's only costing you money (in taxes and utilities).
Best of luck mama.