It's good that you have admitted that you can struggle with anger and that you have reached out to a therapist. I also think it's helpful that you have come here for support and to vent. Always keep in mind though that you will get different opinions and none of the people that are posting are professionals. So, it's important that while you consider the different input you get here that you also consult with your therapist.
That being said, some of the behaviors you have described in your wife are troublesome IMO. I was reading about women and cheating last night and women often cheat for different reasons then men. Women get lonely and often what they want is companionship whereas men usually cheat for the sex and often don't even love their mistresses. So, I thought about how you described your wife wanting to show you video of a trip and something they did with the children. And then how she got mean about having sex maybe many times. Well, some people have a terrible way of communicating what they really want and sometimes what they actually do is hit the other person in mean ways with comments that only end up hurting and confusing them instead of helping them understand something better.
I think what she has been trying to show you is what she really wants is the companionship. And you have already explained that you tend to show your feelings in a physical way. It seems to me "that" is what she is attacking. I think your wife was lonely in her marriage and that is a common complaint with women. I think that is what she doesn't want to go back to, being in a marriage with a controlling husband and being lonely. I think about the movie Sabrina where she asks Lynnel "you work and do this and that, but where to you play?".
I think while you were gone on deployment her ego was hurt but she also spent time with others that knew how to "play and have fun". Often what happens that is so common in human beings is how in a group or a marriage one can slip into a role and that is what becomes expected and begins to get boring and lonely. That is probably part of the reason that the percentage of couples that at some point cheat is high. I am sure you have heard the saying "couples who play together stay together".
You are in the service Dad, and you have a routine, but "where do you play?". You sit and read your sons a story, but do you "play" with them too? I have a feeling what your wife is talking about is how there are other men out there that know how to "play" and you don't so "what do you actually do?". So, take some time and sit and do a review of what your marriage was actually like, "how much play existed in your marriage?".
Do you plan things to actually do, like a trip to the beach, a night with the boys playing minni golf, taking your wife out to dance, all go to a museum, plan a little mini trip for you and your wife that isn't just about dinner and sex but includes some fun things to do together. Do you look to initiate hobbies with your sons at all?
What did your wife want to show you in that video, "we went here and played a game of mannequin". Key word "PLAY".
I have seen other problems, and your wife isn't communicating very well either, just trying to listen to what she does tend to say and what her "hidden" messages are about.
http://www.webmd.com/balance/feature...-your-family#1
https://www.menprovement.com/101-fun...ur-girlfriend/
http://www.huffingtonpost.com/robert...b_1936934.html