Leave her. Let her be happy without you. Sounds like you're a wet blanket on her vibrant social life.

If I'm understanding your situation correctly, you're in the military and she's stuck bored at home. Joining the military is a really good way to kill a relationship. She's already going out drinking (even though you forbade her from doing so), her getting off with another guy isn't a stretch (I suspect you already think she's fucking the guy she's getting the alcohol from).

It ain't going to work. You're already thinking that it isn't going to work. You should be kind and save the both of you a lot of time and heartbreak by ending it now. She wants to have fun and live her youth and you're not sure you can trust her (and you being away in the military only makes this trust issue bigger).