When somebody dumps you and starts a new relationship right away, it often means that there was some cheating going on before the dumping.
Sounds like this guy got himself into a very dysfunctional relationship, judging by the change in his behavior. If you got back together with him, you would probably be disappointed with him. And going by his recent behavior, it sounds like he is still on-again/off-again with the other woman. Do yourself a big favor and ignore him.
Good decisions come from experience. Experience comes from bad decisions.