Normally you cannot boycott another Muslim. It is even worse if this is a family member. People usually boycott others out of anger. However, you may boycott someone only when there is a legitimate fear that speaking to such a person and keeping in touch with them will harm you or others in some way. Therefore, if the situation is as you claim, it would be allowed to generally avoid the person, but try to at least respond to their greeting of as-salāmu ʿalaykum (peace be with you).
What the Qur’an and Sunnah Say
You cannot boycott another Muslim because the Prophet said: “It is not lawful for a Muslim to cut off his brother for more than three days, so that when they meet they turn away from each other. The best of them is the one who initiates the greeting.” [Bukhārī #5727, Muslim #2560, Tirmidhī #1932]
The Messenger of Allah said: “One who breaks ties will not enter Paradise.” (Sahih Muslim # 2556)
What the Scholars Said
The Andalusian Imam Ibn ʿAbd Al-Barr [d. 1071 CE] explained that there is an exception to boycotting when there is a legitimate fear that speaking to such a person and keeping in touch with them will harm you in some way, because peacefully avoiding is better than harmfully interacting.
Shaykh Mustafa Umar