Most Helpful Girl
It seems to me like you only really want this girl because SHE has moved on and you haven't. You haven't found any other girl that makes you happy,so you would rather go back to what's familiar...your girlfriend whom YOU dumped,but who also happens to be a bit emotionally and psychologically unstable. You said she is "good" now,but who really knows.
I believe relationships can have a second chance,but NOT for the reasons you are specifying. I truthfully do not believe you have intense feeling for this girl,otherwise you would not have broken up with her in the first place. Its a power game. She has taken back her power and moved on from you and now you can't STAND it. She said she would wait a year for you. And to be honest,I believe that if you didn't see her with this other guy,you would have been in NO rush to snatch her back up. As long as you knew she was on the market,you wouldn't touch her with a ten foot pole. But NOW,you're jealous and being competitive. The very same things you didn't like about her,are possibly things that didn't change...mind you. Maybe...maybe not.
I think you should leave her alone. You broke her heart because you didn't want to work on things the first time around. Let her move on without you. You had your chance,and honestly...i don't think you deserve another. Good luck.