While I don't have any personal experience with this, my boyfriend M is preparing to sue for full custody of his daughter (her mother is untreated borderline personality disorder and the environment/instability/emotional abuse that goes with it), and the most important thing in his eyes (and his father was a judge) is to keep the focus
100% on the safety and well-being (physically and mentally) of your children.
If you can keep your composure and keep the focus of your arguments and statements entirely on them, the vindictive parent will reveal himself, and if there's something a judge can't stand in custody battles it's a vindictive parent.
This is just what I've learned from talking with M, of course, but considering his background I figure it's useful.