I am not quite sure what to tell you. It sounds like the relationship is already over. She left. She has started dating other guys. And you are fooling yourself if you think she left because of that one fight. I am sure it has been building up for her for a long time.
Right now, the issue is not her, it is your children. You need to figure out how to handle things about them. Custody, visitation, etc. You need to make them the priority right now. Stay civil with your ex, but I wouldn't concern yourself with getting back together with her at the moment. Chances are it isn't going to happen, so you have to figure out how to make the best of the situation and how to do what is right for your children.
Good luck.
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