trade support for the house?

Joshua's answer sounds pretty right on. Funny thing is though, USUALLY, take that term as what it says, "U-S-U-A-L-L-Y" If you get the kids, you get the house, and you will get child support regardless, the courts will do whats in the best interest of the children, and taking them out of their school, moving them out of a house, and dealing with a divorce of their parents, is hard on children, so he might be ordered to continue to make the house payments for the next year or so, and child support will also be paid to you. It might give you enough time to decide just what it is that would be in your children and your best interest. And I would look into what the market in your area is doing, a guy posted today and said he will be loosing $60,000 because the market is not very good right now.

I am not specifically familiar with California Law, however in most states child support is statutory and a separate issue from asset or property division.  You need to check with a lawyer or Certified Divorce Financial Analyst familiar with CA law.  Some other issues to consider.  Can you afford to keep the house on your own?  Why is it important to keep the house?  If you do keep the house and you are both on the mortgage don't forget to consider the fact that your ex will want to get off.  You will have to reapply for the mortgage.  Will you be approved?  Should he share in the cost of refinancing?  A recent client paid over $2500 in fees and closing costs just to get his ex off the mortgage.  This needs to be considered as part of the overall picture.  Also, consider your long-term goals.  Most people going through a divorce think about here and now and not where they want to be in 5 years.  Is your ex trading the house because home values are sinking and he wants other money that may be doing better?  Just some thoughts to consider.