I don't think it has to come accross as revenge, so long as you make it clear you were just looking to see what kind of recourse you had, and along the way found yourself fascinated with the topic. Or you could go the route of "this happened to me, and I'd like to work to make sure it doesn't happen again"
But you do have to be sensitive about the revenge issue, you don't want adcomms to think you are an angery person out to use the law to get satisfaction.
This seems like a good topic for a PS, but you might also have too much, maybe you need to split things up into PS/DS (child support enforcement law/personal experience).
I might also caution you that you may be running into the issue of TOO much honesty. You clearly had a difficult experience growing up, but you can't only write about your childhood or it looks like a desparate cry for sympathy.
The best advice I saw was "PS shows WHO you ARE; DS shows WHERE you CAME FROM." and "Show, don't tell."