I'm not a vet and I don't have PTSD but my girlfriend and I had some pretty similar issues to you with this episode. I think, thankfully, the episode doesn't seem to expect us to think that M'benga was "right" at the end, or to be happy about what happened, and the final scene between him and Pike is critically important because I don't think Pike is supposed to look foolish in that scene. Absent that, this episode would feel really gross to me.

As it is, really the only way I can work with this is knowing that the actual arc here is the enormous one that concludes with Star Trek VI, a movie that I feel only gets more radical with every year that passes and every rewatch I give it. Kirk's realization that he has to let go of all the pain and anger in that movie and allow the world to move on and healing to begin is, when you get down to it, maybe the most optimistic and important message the franchise has ever really tried to express, and if this episode exists as a "middle chapter" between the war itself and that eventual endpoint...well...I can work with it as that middle chapter. But I still feel pretty crummy about it.