I'm so sorry to hear that you're going through this, I am currently in a very similar situation myself (husband had affair and refused to end it and is now seeing this girl, we are separated)
I can honestly say that from my experience, trying to communicate with your wife to ask her to come back / end the affair etc will only push her further to this other man, you have to disengage with her completely- I have 2 very small children and all I do is send Text messages to my husband re the kids and discuss children briefly when necessary. Not communicating with him has been the best thing for my sanity, I'm concentrating on me and the children, making me happy again and I'm actually starting to feel alright about myself. Don't contact her!!! Make sure that when you do see her, you seem happy, busy and look good! That always makes me feel better about myself, plan nice things to do with friends, treat yourself to something or a day out, enjoy your children- all of these things will Make you feel better about yourself, in turn my husband has treated me much more respectfully (although he is still with the OW) and I am actually finding that I am starting to actually be happy!
Me 35 H 38 Married 4 years together 13 years Affair started sept 2015 BD 15th Nov 2015- husband left that night son age 3 daughter age 1