What is the ruling of Islamic law regarding boycotting one's sister's husband who mocks the questioner's family, interferes in their affairs, curses, and violently expels the questioner, while maintaining ties of kinship with the sister?

Islam encourages benevolence towards Muslims in general, and this is especially emphasized for those connected by kinship or marriage. The Prophet (peace be upon him) recommended benevolence towards the people of Egypt because they have a covenant and kinship. If what was mentioned about your sister's husband and your sister's ill-treatment is true, then this is impermissible. You should seize the opportunity to thwart Satan, who seeks to sow discord among loved ones, by practicing piety and patience.

Regarding estrangement from your sister's husband, the general rule is that it is forbidden for Muslims to shun one another unless there is a legitimate Sharia-compliant reason. If associating with him brings harm in religious or worldly matters, then it is permissible to shun him, and the slightest connection, such as greeting him with peace, suffices. As for your sister, be keen to maintain ties with her and advise her gently and kindly. It is not necessary to visit her in her home; rather, maintaining ties through phone calls and inquiring about her well-being is sufficient.