I am not a success story but my story is similar to yours. Not identical..just similar.
First and foremost: Take care of yourself and your kids. Period. That's what matters most right now.
Second: Decide what you want. Do you want to save your marriage? If so, then don't antagonize, don't provoke and don't go on the attack. Look at every thing you say and do through this lense. Is what you are saying/doing going to push her away or bring her closer?
If you want to end your marriage..if you are honestly done..then protect yourself, protect your kids and protect your money.
If you don't know what you want to do then you need to be patient and figure that out. I would say that the kids should be with you in what they know as "home" until you two can get this sorted. That's what I'm doing. Our son is with me until the end of school. This summer I'm changing jobs and he's moving to where his Mom is working. It's not fun, it's not easy but it's the closest thing to a "normal" change of events that we could manage. I still want my marriage to work so I'm giving some concessions and not digging in my heels on much at all. But, that's because I honestly believe I know what my wife needs from me right now and that is support and understanding. Even though she says she's "done" and "desperate to sever the relationship" there are other signs/signals that she is doubting that as the "right" decision. So, my anger is mine. I deal with it. I don't vent, I don't retaliate...my anger is mine.
I need to be the kind of person she wants to be around, wants to talk to, wants to share things with...right now, that ain't happening too much and that's hard.
For you...decide what you want. If you want to save this marriage then you're going to have to let her go for a bit with the full understanding that she may never come back. That's a hard pill to swallow but it's the truth. There is nothing you can do to MAKE her stay. She has to WANT to stay so it's up to you to create a person and an environment that she wants to be a part of.
Hang in there...read through this forum and read the Divorce Remedy by Michelle. It's got some really good information in there.
Best of luck to you...you're in for a loooong ride.