First.......do not contact her parents. I have had ex's do this with the very best of intentions, but it has always served to annoy me. My mother still brings it up years later about how "poor Ty" or "poor Jared' called her to thank her for her kindness (seeing as my mother is a lunatic....this was even more annoying). I know you see it as the mature and respectful thing to do, and it is, but the end result is less favourable. If you feel you must say something, try appearing somewhere you know they will be and let it appear to ahve been natural or coincidence.
Secondly, she sounds like a very confused young lady and you have every right to feel betrayed, naive and hurt. I had adored a man for years, and when I was twenty-four he came to visit, planted a wonderful kiss on my lips and proceeded to break with his girlfriend of five years. I panicked, and ran away and our friendship has never recovered. I was not ready for a real man at that point, and your ex, having a young child, a mature boyfriend (you), may have felt the same......it was all too adult for her.
Yes, many women do love a good chase. It's the ones who hide their feelings who make us crazy, but crazy is not love. It takes time to realize that, and also to become bored with self destructive behaviour. Let her go. Try and find a woman who has it a little more together. This doesn't necessarily mean older, but more focussed. Good luck to you.