Welcome to the boards, sorry you find yourself here but you will get good support here.
My sitch is almost like yours, my W got involved with old friend, turned to EA, I exposed the A to SIL and my sister and my mom. Exposing to her sister not too bad, but with my mom and sis I'm regretting but what can I do it's done now. I did it out of anger then.
For your kids be as amicable as possible, you don't want to be fighting about them now. So to be clear, what you're proposing is that you won't have the kids on the weekends? Are you sure you want that? Consider the long term when the kids start to go to school M-F. Then you would want some weekends with them, IMO.
Exposing the A is not your last chance, although I'm not advocating exposing the affair. She will blame you anyways on a lot of things just focus on yourself and kids and your 180s.
Regarding your funds, IMO you should separate.
Good luck keep posting.
Newman
me40; W43 M18; T~20 D18; S13 & S3 bomb 5/9/11 EA busted 4/30/12; 9/4/12; 4/29/13; 6/10/13 same OM
Separated 4/1/14
"Even a flicker of light will shine through darkness-12/25/2012"....better days ahead.