Lots of people here have heard the exact same words you are hearing now. My wife also did everything you are describing. BTW, connecting with ones friends is not necessarily a bad thing. I found that after the bomb dropped, and to this day, to an extend, I am hyper-sensitive to many things my wife does. Might you have said, pre-bomb, hey, she's getting in touch with her friends...good for her.
Your wife might want to just get out of the house and away from the pressure cooker of you and the kids. She might want to FEEL single for a while. She may want to vent to her friends. My wife drank herself silly a few times and got nasty. They are hurting. They will do things they don't even understand. For now try to chill out, fix you where you can and wait and see what happens. Try not to stir the pot. Get and read The Divorce Remedy.
Stop pursueing, pushing, and lay low. Be pleasant and present, but not overbearing. Be the best father to your kids you can. With regards to your moving out, try NOT to make statements like "you will not leave and NEITHER WILL THE KIDS". That will just turn things into a pissing contest. There are different theories on leave/do not leave. I am not sure which is best. Being advesarial with your spouse is bad in all cases. Next time she brings up. Perhaps ask her for time to think about it or tell her she could leave if she wishes.
DON'T SNOOP. I got busted snooping. I learned a lot, what I learned caused so much stress I didn't sleep for months and I am still paying for the snooping. The violation that my snooping represents to her is now perhaps #2 on her list of issues with me. DON'T SNOOP! You will make yourself crazy. You will have to live with what you learn or confront her. Lose/Lose
Best of luck. You will probably endure much suckage but DB can work.
Me 44 She 46 S13 D9 M18 T23 3 years DB'ing Successfully busted