I'm sorry about how stressful this is! I agree that for the boys' sake, if she asks you if you're going out a simple "yes" or "no" would be better than asking her why she cares or something similar. Try to keep things business like and to the point versus taking the conversation in a new direction.
Regarding "legal posturing" I'm telling you there will be no "he said / she said" even if this goes to trial. The judge doesn't care who was right and who was wrong, or who is the better parent or anything else about your personal lives. His or her priorities are (1) protect the kids, (2) uphold the law, (3) make sure that no one is being steamrolled or taken advantage of via making sure that your asset division and support agreements are as fair as possible and inline with state formulas.
She could have had 10 affair partners, called you horrible names, pushed your food on the floor every time you tried to eat and it just wouldn't matter. If you can take those worries off the table it will make dealing with her much easier for you.
Acc
Married 18, Together 20, Now Divorced M: 48, W: 50, D: 18, S: 16, D: 12 Bomb Dropped (EA, D): 7/13/11 Start Reconcile: 8/15/11 Bomb Dropped (EA, D): 5/1/2014 (Divorced) In a New Relationship: 3/2015