Sepparated spouse is dating should I just give up?

My wife and I have 2 kids 2and 3. I was the primary care taker of them while we both finished college, Within 3 mos after the her graduation she convinced me that we should move to another state where we could both financial stable. I was still in school and decided to go along with it and move her and my kids then join them two months later. within those two months she told me that she needed space and had been dating, having sex with several people , in love with one and never came to my graduation. now 10 moths later she is still dating but wants m to move closer for my kids and to see if we can work on things. I gave in again and went down to visit for xmas and got attached all over again only to find that she has a separate phone from her main phone with tons of numbers from different guys from the clubs and bars that she frequents. I feel that I should finally get that divorce. I really would like to reconcile but shes hot and cold
confront about the jerks shes dating or never say anything? and file.. i know if i say anything its not going to stop her , its going to let her know that I know and thats it!

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