Brother,
Similar curcumstances here: I am an infantryman here in eastern NC (though a Marine at LeJeune). Have been hiking/backpacking for years but just took my wife on her first backpacking trip two months ago. I had considered the Neusiok Trail in the Croatan for an easy introduction, but I just didn't think it would be satisfying without mountains.
We went to the Shining Rock Wilderness out towards Asheville/Brevard. I have been there many times. We had a great time! She only carried about about 15-20lbs, we kept it low miles (like 5 per day). I did all the camp chores (set up tent, cooked dinner, hang food, fetch water, etc). Also tried to suprise her with some snack she would like, hot cocoa in the evening, etc. End result she was eased into it, had a great time and now has an interest. She wants to challenge herself and "carry her own weight" next time. I have either solo'ed or have taken my son in the past, but the expereince of going with my wife (and best friend) was fantastic.
Try Shining Rock/ Art Loeb Trail. Lots of routes/loops you can choose with great views and as challenging as you want to make it. It will a great way to decompress after returning home and is the best medicine you can have.
Be safe brother
Semper Fi