Jets,
First, I commend you on the efforts you are making and letting God do His work. But that does not mean that you dont have work to do.
First off, knock off the invitations to do things as a family. You are in Plan B...she has left the family. Yes, she is still their mother and she should be afforded all reasonable time with them. But her time with them does not include YOU! And you dont get to have ANY time with her...period. Okay? With this guy gone for 6 months, she will use you to keep the home fires burning until he gets back. It is better if she sits there alone, with neither of you. It will give her better perspective in the fog, and no OM to keep feeding the fog.
On contacting the Navy (I assumed he is in the Navy...or the Marines), you must DO THIS! I was an Inspector General in the Army. If someone had reported a solider as having committed adultery and still committing adultery, and the command had given that response, we would have been up that commander's you-know-what so fast he wouldnt know what to do. That response is unacceptable, and that commander figures you will just buy it and walk away and be quiet.
Contact the Navy IG. They have a similar system there. Report this guy, and make it VERY clear that your next stop, if this sailor is not ordered to cease contact with your WW, that you will be contacting your congressman/senator. We used to get (and hate!!) congressional inquiries all of the time. If we had a choice, we would rather take care of it before it gets to that level.
That commander will not want the IG involved in his command, so he will order the sailor to stop seeing your wife. That is the law (UCMJ).
On whether it will affect your wife...well, of course. You are asking someone to order her cake from being put in front of her to eat. She wont be able to see this guy, otherwise, he will go to jail for disobeying an order. Will she be happy at this? Nope. But again, that does not matter. Exposure is exposure. WSs always take exposure as BSs being vindictful and spiteful. We arent, but that is what they believe. BSs always are scared to expose because we believe it will cause the WS to run to the OP. Well, THEY ARE ALREADY WITH THE OP!! You cant make them run to where they already are. But in your case, you are lucky. Why? Because someone can order the end of the affair, at least until your wife is divorced. So use it!!
Sitting back and just hoping since OM is gone that she will want to come around is a BS kind of fog. It wont happen that way. Shoot, my wife was home for 18 months with NC with OP (he had moved back to Florida). And when our recovery soured and we separated, it only took a week before they hooked up again. Such is the nature of addictions. Of course, in my story, two weeks later we went to court and I got primary custody of our kids...which blew the fog completely away. Leading to our recovery now.
But, if I could have had someone order the OM to stay away from my wife? I would have gotten that done in a second. This is an addiction. If she was addicted to cocaine and you could make sure that there wouldnt be any cocaine around...would you just sit back and say "gee, her drug dealer is gone for 6 months. I sure hopw she will use this opportunity to clean up and come home?" Or would you use the opportunity to have someone make sure that dealer does not come around again, to force your wife into withdrawal...and possible recovery?
Call the Navy's IG. Report this. Take it as high as you need to go. Be a nuisance. Believe me, they will tell this guy to knock it off because they dont have time to deal with crap like this...they have a war to fight.
Then let the dust settle. Let your wife be alone, with OM gone and ordered not tot alk to her or see her. Plus, she has no contact with you.
This is your best opportunity to possibly get your real wife back. Any other way is just feeding the addiction. And that guy WILL be back. And everything will continue as it has.
And as a side note...that guy does not belong in my military. He has no honor, no character in doing what he is doing. I would not want him in a foxhole next to me. His selfishness will only get someone killed. So report him. The ilitary is VERY good at weeding out the ones that do not belong. And this guy definitely doesnt belong.
In His arms.