First, thank you for your service to the United States.
I’m not a lawyer.
You may be right that those emails may now be inadmissible in a trial… I’m not sure how the rules of evidence work in this state… they may be “fruit of the poisonous tree” to borrow a phrase. That is to say, because you obtained knowledge of these emails through illegal means you may not be able to turn around, obtain them legally and use them at trial. I would DEFINITELY talk to a lawyer about it.
One thing you may want to try is military law. You seemed to indicate that the person your wife is seeing is in the military as well. It is my understanding that the Code of Military Conduct prohibits any soldier from committing adultery. It may not help you out on the alimony side (I don’t know if you can use judicial rulings from a military court in civilian court) but it may stop the affair (if you want to try and patch things up with your wife) and will certainly put a crimp in his life and could expose him to a court-martial.
Hope that helps.