How do I switch owners on a house?

You cannot quitcliam away his interest, only he can. If he will not, your only other option would be to file some sort of action to see if the court would compel him to convey.

Unfortunately, it sounds like the original set-up of this arrangement was not well-advised. Regardless of which of you had custody, putting title in his name alone was an invitation to trouble.

You should consult a local litigation attorney to see what might be feasible in your state. And, even if title were somehow conveyed, the second mortgage would still be an issue unless the court were to force him somehow to pay it off.