How can one deal with a cousin from the paternal or maternal side who is characterized by a long and hurtful tongue, without severing kinship ties, with the desire to stop his transgressions without responding in kind or resorting to estrangement?

You can supplicate for your relative’s righteousness and advise him with wisdom about the importance of guarding the tongue and the danger of letting it loose. If he does not desist, you may abandon him for a legitimate Islamic interest. Maintaining ties of kinship with an abusive relative should be done only to the extent that it does not cause harm. Hating a disobedient person for their disobedience is an act of nearness to Allah, as the Prophet, peace and blessings be upon him, said: “The firmest handholds of faith are: loyalty for the sake of Allah, enmity for the sake of Allah, love for the sake of Allah, and hatred for the sake of Allah.”