This is a perfect example of a character who has a ton going on and would really benefit from a full analysis. However, I'll do my best with this mini-assessment to make it worthwhile, I hope.
First and foremost, a reaction of freezing in place when faced with a gun or "flintlocks" as they were is totally reasonable. That would be a trauma reaction to an inanimate object he had previously witnesses carnage as a result of its use. In particular, watching his father's hand explode would be highly traumatizing, and no doubt would result in a complete revulsion of a gun.
What would this look like? Not wanting to touch one, carry one, be around them, have them in his house. He would likely show hypervigilance and paranoia when other people carry them or shoot them in close proximity to him. He might have nightmares of the event, or even reenactments of the trauma during the day (i.e., visualizing it happen when around open fields with carriages). You can safely say he'd never set foot in a duel field ever again. Very realistic...and likely not something he would get over for a long time, if ever.
As for forgiving his mother...it would be tricky, but if you could write it well, I saw a great character arc for him to not only forgive his mother, but also his father for his "stupidity" for putting his life on the line. What if Nathan had someone for whom he would protect her honor...no matter what? If Nathan could somehow be put in the shoes of his father...who clearly loved his flawed mother, and was willing to die for her. Having him learn the lesson that no one is perfect, and that yet people are still worthy of sacrifice. I think he could do it.
It was rather unclear from the intake form that Nathan really suffers from guilt of not stopping his father (from the duel, I presume). However, if he does indeed feel guilt at sitting atop the carriage and not stopping the duel, I would think it would have the opposite effect on him wanting to act like a wastrel. Punishing his mother by acting like a dandy would hardly honor his father's name. Don't have time to go deeper here, but I hope you get what I mean.
Thanks for writing in...I realize you wrote in many, many months ago when I was slammed with mini-assessments. Thanks for your patience, Robin!