You've done pretty well these last few weeks getting to the bottom of things. What you've told us: your long-married wife had an emotional and physical affair with some asshole, lied to you, took the affair underground. It took you threatening divorce to snap her out of it. She's blown your marriage up. You've got kids and would like to repair the marriage.
Now what?
1) Try to get to the bottom of your wife's awful behaviour. Individual counselling for her to understand what the hell is wrong with her, and adopt strategies to fly right from now on.
2) I think you need to be a bit selfish in your marriage from now on. Look, having read many stories like yours over the years, there is a significant chance your wife cheats again. Sorry to say that to you, but it often happens. I advise you to undertake a program of self improvement and learn/relearn to do things that make you happy, do things on your own and with your friends. You may well find yourself divorced, start working on a 2.0 improved version of you. If you stay married, great, you're a more confident, attractive man in your marriage.
3) Trusting your wife at this early stage after her cheating is a mistake. She's messed up, wobbly, to some degree still has cheating and the other man on her mind. This is the 'fun' of reconciliation - trying to rebuild trust with a cheater while not trusting her.
4) No matter that your wife pleaded not to talk to a lawyer, I would talk to one if I were you. Get the lay of the land about what divorce would look like for your marriage where you live. And I'd tell her you've spoken to a lawyer, drives the point home you're not OK with her trashy behaviour and she better not take you for granted again.
[This message edited by SnowToArmPits at 12:34 AM, Wednesday, August 17th]