At this point you feel betrayed and you are probably experiencing a lot of emotions, often this can bring out anger too. Anger brings out a desire for action and that is something you have to make sure you hold back on even though you might feel you need to act.

It's good that you found this site where you can vent and actually while you have shared your concerns here, you have also shown to be pretty level headed and considerate. I am glad to hear you are paying attention to your children and how this has been affecting them. This is one of those times where they will need you to reassure them they will be fine and that you are there if they need to sit and talk. Your children may struggle with how your wife is leaving and often children even their age feel like they are being abandoned and even that their parents don't love them enough to stay together.
It's important to reassure them that they still have parents and you are there for them and love them.