I'm not sure about you, but I use my horn to make other drivers alert. Not to try and "escalate" anything. He was turning into me, so I used it in an attempt to make him aware of what he was doing, because he clearly did not check any of his mirrors or look in his blind spot first. There you go, yet again, making assumptions for yourself.
He had already cut you off. You braked successfully and did not hit him. If you had time to lay on the horn you had time to de-escalate and drive away. But as you saw, laying on the horn DID escalate matters and he went into road rage, which YOU caused by laying on the horn (not, evidently just giving a short honk to warn).
Thus you lost control of the situation, stopped your car so your brother could get out and now want to appear blameless. You're not blameless, you need to be a better, more responsible driver and firearm carrier and not let your anger get the best of you. You could have told your brother to stay in the car, not stopped to let him unbuckle and get out.
You posted here asking how you could have handled it better and I'm giving you advice. Take it or leave it. Your methods obviously need improving.
PS - you never did give us a cite on what law in Maine allows you to speed in excess of 80 mph for reasons of personal safety. Please link it.