Cheating wife still talking to OM What to do?

My wife to be and mother of my child was recently caught having an internet relationship with another guy. We fought about it and i asked her to not talk to him anymore and she just rolled her ese and said ok. When i asked her why she did it she told me he just swept her off her feet and said all the right things to her and she cant believe she fell for it. Our sons birthday was the next day so i didn't want to leave so i just made her promise to not communicate with him and forget about him and she said she loved me and only wanted to be with me and out family so she would end it. I figured if we had a strong relationship we could work it out and i would try to do my part and be more romantic to her. The next day we spent alot of time together tiring to rebuild the relationship ETC ETC. The following day i noticed in the history she was searching for him and that that night she did admit she had talked to him again cause he was worried about her but she told my she said it was over. so being the snoop that i am i check the phone to see if there were more text messages and she had made sure she deleted the call logs and all text messages. What should i do? The only time she acted hurt in this mess is when she found out he had lied to her and now she is still talking to him. He lives in another state but i still don't want this to go on but i need to be sure before i end a 6 year relationship and a 4 year old child.