I think it's emtirely possible that dad could be successful at getting a downward modification due to his diability. He's not willfully in contempt. He can't work because of his diability.
Not saying it's a sure thing by any means, but judges have a lot of discretion.
It would also depend on his disability.
I worked for a company that had short term disability which paid 66% of the most recent wage. When you consider that you're not having to go to work, no lunches out, no transportation costs, and (in some cases) no taxes, the recipient wouldn't suffer much of a decline in spending power.
Also, check to see if the person is disabled per SS standards. Probably not, but if they are, the child may receive some benefit, as well.