Does that make sense? I will not be saving SQUAT by squatting here now.
Mathematically maybe it does, at least at the current numbers, but more broadly -- no, it doesn't. You will have to pay SOMETHING, SOMEWHERE for either rent or mortgage. Either this house at its current mortgage payment, this house refinanced or a rental. Between whatever final settlement you reach with your husband and whatever income you end up making in whatever job -- the two of you need to co-parent and come up with a safe shelter for your children.
I'm saying begin putting that plan and budget together now, and using your husband's foolish nonchalance about the mortgage that is in his name -- by NOT PAYING IT -- as a way to transition to the new plan.
Either your husband's proposed contribution going forward is fair and reasonable, as your attorney says, or it's not. It either allows you a reasonable plan for that contribution, plus what income you can reasonably expect to make, to add up to a plan whereby you can provide food, clothing and shelter for your kids . . . or it doesn't. In which case it's time to get a better lawyer.