Whomever ends up with the house, if either of you, won't be buying the other out. There's nothing to buy.
I wonder if negative equity could be used against the rest of the assets? I think so. It is like taking on debt in exchange for something else.
Something to think about.
I think what others have posted if the house is contentious would sound reasonable to a judge. Walking distance to your work, not uprooting the kids.