What should a person do if subjected to insult and slander via a car horn, on the order of insulting one's honor and slandering one's mother, and is it permissible for him to retaliate in kind or with physical force?

It is permissible to seek justice for the oppressed in a similar manner, without transgression; however, forgiveness is superior. Therefore, it is not permissible to slander one who slandered your mother, but it is permissible to curse him. As for the "horn honk" gesture, if it is of the nature of an understandable signal, some scholars consider it akin to explicit slander and divorce [in its legal implications], and therefore it is not permissible to accuse him of slander through it if it implies insulting the mother, nor is it permissible to hit him. The matter can be reported to the competent authorities.

We find it unlikely that the "horn honk" gesture is intended as slander; at most, it would be considered an insult.