What is your plan? To stay in a loveless, sexless, trustless, roommate of a situation for 10 years while your WW has a string of affairs and flaunts them in your face?
Get a 2nd or 3rd lawyer, do what needs to be done, and deal with the consequences.
No, I doubt you'd get sole physical custody. But are you telling us that you'd be denied 100% access to your children? Do you really think that's what your WW would want? Even down the road after she gives up on manipulating you? Would she harm your children by trying to keep you from them and talking bad about you? EVEN STILL all you can do is get a good L, do what you CAN do, and let her deal with her own soul.
I recognize how hard your situation is but this victim crap is wearing very thin. What do you want from us? To all agree that you have been screwed and acknowledge that nothing we can think of to do or say will work because your situation is uniquely unfair, so you have all of our eternal sympathy? OK, you've got it. Did that solve your problems?
You don't have time to sit around and cry into your beer. Your kids need you. You can say "there is no option" but there is. See, time will keep marching forward like it or not. Not to decide is a decision to sign up for more of the same.
Me:38 XW:38 T:11 years M:8 years Kids: S14, D11, D7 BD/Move out day: 6/17/14, D final Dec 15