To be honest, to me this just sounds like two people who don't get along. i don't see PTSD here at all...
My SO is a combat vet with diagnosed PTSD and has some of the same behavior traits you mentioned here: short temper while driving, bouts of anger/frustration that can seem unprovoked, and what seems to be complete disregard for things I feel importantly about. Here's what I've taken away from it.....
He has a short temper and is overly critical of others while driving (especially in traffic) or in crowds because he is not in control of the situation and that makes him anxious. We argue sometimes when he becomes angry over what seems like nothing -- but this namely happens when I am ignoring the signs, whether it be an anniversary, a small trigger, or something else he is concerned about but not dealing with (school, psych appointment, distrust in meds, etc.) and when I don't disengage when I need to. (I have had a problem backing down in the past, when disengaging would have stopped an argument/fight before it started.) As for disregard for things I feel importantly about, this is a hard one for me, but a big part of that is that we are complete opposites in every aspect -- personality, political beliefs, religious beliefs, how we were raised, where we were raised, who we were raised by, etc. Furthermore, the military hardened a lot of things for him, which has resulted in an apparent lack of empathy (I am overly empathetic), hyper-vigilance and distrust (I am over trusting), dislike/distrust of darker skin men who look similar to those he met in combat (I am a huge advocate for loving everyone no matter what). Some of these things he can't change and don't make sense now that he is out of combat, but that's what we're working with. Once I stopped trying to change his outlook on things or trying to convince him to see things my way, it stopped being as much of an issue. I had to accept that he is who he is for reasons that cannot be changed, just as I am who I am for other reasons, and that neither of us will be able to or should want to change the other. Now that doesn't mean I don't make my feelings and opinions known, but I otherwise don't badger him about them unless I see something that is crossing a boundary for me, then I speak up in a clear,non-judgemental way.
From what I have read throughout the forum, most of the other posters here have much more experience with diagnoses, especially PTSD. But this is my own two cents from what I've come to see in my relationship.