Things to think about in terms of affording your home:

Would you buy it today at the price of your current.mortgage? If not, don't hold onto it. If yes ie it was a great bargain when you bought it, or you put a lot of sweat equity into it, or it has great potential for you to build sweat equity in the future, then ask yourself the second question:

Can you afford it? Would you be able to qualify for a refi loan (counting in child support, your income, etc)? If you can refinance it into your name, add up expected .mortgage payment and property taxes, then subtract tax breaks. How does that total compare to renting a nice 2 bedroom apartment in your town?

Can you rent out an extra bedroom after the divorce? Would this make your mortgage affordable?

Don't forget repair and maintenance costs. Much as you may hate to give up your home, renting may make more sense for you at present.

Check out the mr money mustache blog for great ideas on reducing your expenses. I also love the tightwad gazette books, which include lots of great ideas for kids.