A phrase you'll see a lot on SI is, "actions, not words."
People do what they prioritize and typically they prioritize what is important to them. It doesn't matter what folks _say_ so much as what they _do_, because in what they do you see what really wins their attention and effort.
Google this phrase, 'psychology "personal narrative" ', and this one 'psychology, "personal agency" ' (the bits between the single quotes) and read up on those a bit. By betraying you, by lying, she's broken your 'personal narrative', which is each person's story of their life. How they (you, me, everyone) got to where they are now. Personal agency is having full knowledge of what is going on around you so that you can make correct, informed, decisions about yourself. She took your personal agency when she lied and hid things, when she bad-mouthed you to others, and when she talks of one thing to friends and says another thing to you.
As a thought experiment, imagine yourself six months before you met your WW. A friend says, "Hey, BSPheonix, I met this girl you'll like. She's really hung up on a guy now, but in six months she'll be free and then 8 years later she'll cheat, lie about it, bad-mouth you to everyone, and then lie some more. After that she'll play "the victim", not want to discuss anything about it, and then chastise you for being hurt and not getting over it on her schedule. Want to meet her?"
What would you say to that offer? If it isn't the same thing that you're _doing_ now, then really think about why it isn't.
About your kids - I was a child of a sexually, physically, mentally, and emotionally abusive Mother and a Father who didn't really know how to relate. FOO has a long tail. Anyway, Mom and Dad got divorced. I was ecstatic and lived with Dad. Mom and Dad decided to annul the divorce. I, at 15, cried, sobbed really, about it when I was alone. It was back into the fire for me. So don't assume that you'll be doing the kids a disservice if you leave. Really think about why you're deciding to stay. I'm not saying leave or stay, I am saying really think about why you're doing what you're doing and -then- think about why you think that way. Introspect deeply about your own "whys".
Anyway, once you've got a handle on personal narrative and personal agency, and the trauma that results from losing them, then go up to your PhD wife and say, "Why did you think that it was okay to break my personal narrative and take my personal agency by your actions and words?" and, "And why do you now say that you have nothing left to 'fix' in IC if you can so casually break someones narrative and steal their agency and then berate them when they don't get over the trauma to your timeline?"
I do wish you the best of luck, BSPheonix. I hope that it all works out for you, and soon.