I am wondering if you can setup a living trust and put the house in the trust, or make some other arrangement (e.g., putting your kids' name on the title), to make sure the house can only pass to your children after you are done using it. (You need to talk to a lawyer for specific arrangement.) In this case, your hu*****and probably is more willingly to let you keep more money under your name; after all, it will belong to his children in the future.
(This arrangement will also make your next marriage easier.)
Lawyer is expensive. If possible, try to settle -- for the benefit of everybody.
As to child support, your hu*****and needs to pay anyway. If he has less income in the future, he can ask to pay less in the future.