Please look at all your options. Depending on your work history you may be entitled to spousal support along with the child support. I know the US, Australia, England and many other countries have spousal support(alimony) so there's a chance he might have to pay enough that you could keep the house.

If he cries that you are draining him, that you are being greedy etc... remind him he did this. It was all put in motion by his selfish actions so now you have to do what's best for you and your kids not him.