the question is, do you want to? if not, then don't.
there's something i didn't understand with the story. you said that the father of the baby is also in the army, and that if this were to be found out, they'd be both kicked out. but then he wants a part in the baby's life and to give him/her his name, in which case, they would be practically announcing to the world what they did. in my opinion, the only real problem here is the legal issues concerning the baby.
i don't believe in "once a cheater, always a cheater." if that's true, then we're all to be branded cheaters. no one is innocent.
the most common mistake couples do is counting what they give and what they receive. don't make it into a contest of who screwed up more. you pushed her away. you have to understand how much it hurts to feel unneeded. emotions know nothing of reason. you did the same when you're annoyed and shooed her. you knew it was wrong but you did it anyway.
marriage is about two people being joined together. "for better or for worse," not "for good or for better." you don't just ditch your partner because he/she made a mistake. it's a commitment and a responsibility. you signed up for it.
to everything however, there's limit. some things just don't get fixed. if you're at the end of your rope, then there's no point dragging on the suffering. but please keep in mind that divorce affects not only the couple. a broken family isn't healthy for a child. every kid dreams of fairy tale endings.
i suggest you consult a marriage counselor before deciding.