Also - consider the following issue:

If you stay in the house and H pays half the mortgage and upkeep until the kids are 18 - what happens if you get into a new relationship?

My divorce decree has the (very common in my state) stipulation that if I cohabit with a man, I can lose my alimony. I didn't think it was a big deal since I wasn't really looking to get married again. However, there have already been situations where I would like to help a male friend out by offering them a place to stay at my house, but don't dare because I know my ex would try to make a case that we had something going on.

So you might need some kind of stipulation that you can buy your ex out at any time before the kids turn 18, or that you're not restricted in who can live there, or - I don't know how best to put it, just wouldn't want you to find yourself in a pickle a few years from now if you are in a new relationship. Something to discuss with the attorney.