I would try to keep this thread going here in Newcomers. You should get more traffic on your thread here.
Your wife must look within in order to solve her issues. There is NOTHING you can control to make this happen. It is her journey, and you are now on your own journey. Work on yourself and fix that which you need to work on. Read about detachment, and start LRT.
It is very possible what she has said is true, that does not mean she is going to come running back to you. Get out and GAL. Be the best DAD that you can be. Your children are the most important thing right now.
If I understand you, you stay home with the kids and your wife works. If she move out what consequences will that have on your finances? You need to protect your children.
