I had this a few years ago with a kid involved too, a deeply unpleasant experience. Here is my tuppence worth.
1) Be civil to her at all times even if she starts.
2) Get a younger, more attractive girlfriend.
3) Do exciting things with the kids when they are over.
4) Always give the impression that you are doing great. 2)should help.
These things should be enough to wind her up lol.
Also, if anyone needs any advice on how do deal with the Child Support Agency give me a shout. I know all their tricks and I have a few of my own.