When I discovered that my xh was cheating, I was furious! I did all of the wrong things until I came here and learned the principles of dbing. Once I got a handle on my emotions, I came to realize that I had absolutely no control over what he did, but I can assure you, when he kept crying the blues about leaving, one night, I came home and told him that he could leave. He sat on that sofa and cried like a baby. Two weeks later he was gone. Once he was out of the house, everything came to light and I went into business mode.
I didn't have to tell my parents and sister what was going on for they had caught a glimpse of him on the road with the barfly in the vehicle. Looking back now, I laugh at the all nighter that my mother and I pulled packing up all of his stuff in those nice black plastic bag luggage. He used every excuse not to come pick up his stuff. I gave him a week and if he didn't pick the stuff up, it was going to the dump. He knew I meant every word of that. It took us 2 1/2 years to get divorced because he kept dragging his feet and yet, blaming me for all of the delays. Once it was over, I was finally free of the stress and looking over my shoulder and asking myself "what's he going to come up w/next".
I have read that sometimes it's better not to tell too many people what is going on w/the cheating, etc., as it makes it harder for them to come back. Others have made a point of tell their parents because the questions do tend to pop up as to what is going on, etc. You have to decide whether you want to tell them or not.
As for your children, it is difficult for them to understand and I certainly hope that they do not think that they were responsible for her leaving. At some point, it all will come to light. The best thing you can do is not to talk to them in a negative manner about their mother. Your children are smart and they will figure everything out and they will need to determine what kind of relationship that they want with her.
Treat your situation as a business deal gone wrong. Keep tabs on your bank accounts and credit cards if she still has access to them. I wouldn't discuss anything with her except for the bills, etc. She's gone for now and she really does need to find herself. For now, keep the focus on you, your life and your family. Some day, she may regret what she's doing...but for now....she's off in la la land.