Is severing ties with the wife's cousin, after he has caused offense, considered a severance of kinship ties?

The wife's paternal cousin is not among the husband's kin, but he is among the wife's kin. The texts that forbid cutting off ties of kinship do not include the husband, but they may include the wife if maintaining ties with him is obligatory upon her.

It is not permissible for a Muslim to abandon his brother for more than three nights, as the Prophet, peace and blessings be upon him, said: "It is not lawful for a Muslim to abandon his brother for more than three nights." The obligation is to reconcile between people, unless the abandonment is due to a deficiency in religious commitment or immorality. In that case, advice should be offered, and if he does not respond, there is no harm in abandoning him, especially if there is fear of harm to one's religion or worldly affairs.