Don't involve the kids and use them as a reason for her to change. That is manipulation by trying to guilt her back. If you want to save your marriage, keep the road home paved smooth. Outing the WW may make you feel justified and feel good short term, but think about it long term. How hard would reconcile be if everyone knew and told you that you were a fool for taking her back? How would she feel that you told everyone, and most of all, how would you feel for not holding this in like a man, and just dealing with it personally? If you need to confide in 1 or 2 close friends of yours and not hers, then do so if its safe for you.
Everyone will have different opinions. If you don't plan to recon and you're sure to D, then I don't think it's a bit deal if you are 100% sure.
H 49 , W 47 T 23, M 17 S11, S5 BD: 7/18 IHS: 7/18 - 3/19 Physically Separated: 3/19-4/19 Piecing: 4/19 - Current