@JSSavage,
First of all, I am sorry this is happening. And this is, unfortunately, not the first time a soldier being deployed has been cheated on. It is a stressful situation no matter what.
You already have all the information you need. And in the US, pretty much everywhere, you can get a no-fault divorce. You do not need to prove cheating. So cut that out. You're done doing that. Anything else you gather up would be for shock and punishment value, and to feed the drama.
Same thing with waiting around for some 'gotcha' moment with this guy. You have already become your wife's judge, jury, and executioner. No sense in waiting around for her to give him another BJ or whatever. I am not excusing her behavior at all but waiting for a 'gotcha' moment serves no purpose other than to punish and amp up the drama.
A divorce is drama and punishment enough.
So cut it out. And instead, quit focusing on how hurt and pissed off you are (and I am not saying you aren't justified in feeling either of those things), but instead concentrate on your daughter.
Build the best possible post-divorce life for her that you can, and that means not being a total dick to her mother, no matter what the mother deserves. Because your daughter, inevitably, is going to get older and is going to ask about the circumstances leading up to her parents' divorce. And you can take the high road and honestly tell her that you did all you could and you treated her mother with decency and respect and were shat on for your troubles, or you can tell her that you were petty, nasty, and vindictive. Or I suppose you could lie to your daughter.
Why wait? Why play games? Call your lawyer now (you should be able to get a referral from your base if you don't have a lawyer already). Tell your wife now - and nothing out of a movie - all you need to say is: "It's over. I want a divorce." Period. She will know damned well why you want one.
Everything else is just childish games and it makes you look bad. Want your daughter's respect? Then let an opportunity to be punitive and vindictive against her mother slip by in favor of what is best for your daughter, who is innocent in all of this mess.