As far as the house is concerned, you cannot force him to pay the mortgage. If you keep it in his name and he doesn't pay, the mortgage will go into default and eventually down the road towards foreclosure...whether or not the property is forclosed on depends on several different things, and the time frame varies with the company and state you live in. I would suggest you refinance but if you cannot afford that and are worried he will not make the payments (which happens frequently with divorces as he will see it as why does he have to pay for your place to live and for wherever he is now), I suggest you and he try to sell the property and go somewhere where you can afford to make rent/mortgage payments on your own...
as far as daycare, I am not sure why your daycare is costing you 600/week, you may want to look into other options as far as that is concerned also....