I used to have road rage although not to the point of violence. I honked and sometimes waved at drivers, not using all my fingers . . .
Stephen M. R. Covey wrote in his book, The Speed of Trust, (paraphrased) we judge others by their actions but we judge ourselves by our intent. Shortly after I read this, I had two encounters on the interstate near Atlanta. The first one was a guy cutting me off in traffic. The second one was me cutting someone off. The difference? I was heading home because my son was injured. That other guy? He was just a jerk. Or maybe he was rushing to get to his kid. I have no idea.
The reality is we never know what someone is going through in the moment. Give people the benefit of the doubt and, as you so wisely wrote, let it go.