Unless you were an abusive spouse, I'd be pretty confident that she probably DOES have an affair partner. I'm sorry to say that, but most WASs do, and that's pretty extreme behavior that shows she's been planning this for a while. That's probably why she wasn't enthused about marriage counseling - she was already planning this.
Be really careful to document everything you can, because she may try to set you up for false charges. (Such as false charges of abuse - assuming you're not abusive, as I said.) Save every email and text exchange. Think always about how what you say would sound in court.
Seems to me there's only two kinds of spouses that leave like that - victims of abuse or sociopaths. Read the book The Sociopath Next Door and see if you recognize anything that sounds like her. Someone who was just mentally ill - depressed or psychotic - would not have been that deviously organized about it. Or that pathological. (It's also possible that she's being egged on by someone - does she have a man-hating friend or sister who is this devious?)
You need to stop begging her right NOW. Get yourself a lawyer ASAP and collect all the financial records of everything she took. You're going to have to fight for your kids, and for your fair share. Get her off your credit cards. Run a credit check to make sure she hasn't taken out loans or other cards in your name.
Check the phone records - if she's been having an affair there may be a million texts to one number. This won't matter in no-fault states but at least you would be aware of what you're up against.
Look, I'm not saying there's NO chance for reconciliation - there always is. BUT - someone who would treat you - her children's father - like this in the absence of abuse has a very serious character deficit. I think, if you were to look back on your life with her without the rose-colored glasses, you would start to see that there were red flags flying everywhere. NO ONE goes from being a good person, to someone who would do this to their spouse in the absence of abuse.
