What is the ruling on my assaulting a relative by beating him, as he had accused my sister of fornication, and what should I do if someone insults me again?

Jealousy regarding one's honor is commendable, but addressing injustice should be in accordance with Islamic law, meaning punishment should be commensurate with the offense, without aggression. Responding to verbal abuse with severe beating is an act of aggression. It is permissible to respond to slander against one's honor by describing the slanderer as a transgressor (fasiq), and it is permissible to refer the matter to the judiciary. This is because the implementation of physical punishments (whether a prescribed had punishment or a discretionary ta'zir punishment) is the prerogative of the ruler (wali al-amr) or his representatives, such as judges, and individuals are not permitted to implement them, in order to prevent chaos. As for ta'zir (discretionary punishment), it is within the authority of the Imam and those who have the right to discipline, such as a father, husband, master, and teacher.