I'm a total newbie so take this with a grain of salt (or several), but when I was reading through this latest thing a big part of me was like who gives a **** about the possibility of her coming back or not when she's telling the kids some rando is now their stepdad?! This is probably my emotion talking, but I would sit her down and calmly set up some ground rules for what is and is not OK in terms of the kids. Lying to them is NOT ok.
I don't know what kind of decision-making framework can or can't be set up during D proceedings but maybe it is time to start that process so that you can protect your children the best you can. Having your WAW tell them to keep secrets from you about men in their lives is truly ****ed up and I could imagine setting them up for issues down the line... not to mention you DON'T know what kind of person he is.
My friend's XW's new BF is a total jerk and exacerbating his D11's anxiety to the point where they're now all in family counseling. Anyway, just a knee-jerk response but I might try to separate and prioritize what is best for your kids over a piece of paper that your WAW isn't honoring anyway. Also feels like beta behavior to let it slide in the hopes that she might wake up vs. stepping up and talking with her about it.
Of course talk to your L first to make sure everything you're doing is consistent with getting the best settlement for you and the kids possible.
Me (46) H (42) M:14 T:18, D9 & D11 4/19 - 12/19: series of escalating BDs 9/20 - present: R and piecing