Take this with a grain of salt as I've never been married, never been divorced of course, and have no kids.
Capote, I realize that you and the soon-to-be ex are probably at each other's throat quite a bit. What I have tried to get friends who were in similar situations to remember is that the ex is likely to be the primary caregiver or at least half caregiver to your kids. The less stressed that person is hopefully the better they are treating your children. The less time they are arguing with you or talking to their lawyer about divorce issues, child support, or anything else related, the more time, hopefully quality time, they have with your kids. Do what you can to get the animosity out, don't fight in front of your kids, don't talk negatively about the other in front of your kids. If your kids believe that it's just something the two of you could not work out all the better. At some point, if they are used as weapons against each other (you and the ex), they will know how to use you against their mother and vice versa. Hopefully the less pissed off the ex is now the easier it will be in court as well.
Just my two cents.