Is it permissible to boycott a mother who has been proven to have committed zina (adultery/fornication)?

If a mother's adultery is proven, she has committed a grave sin. It is obligatory for her children to maintain ties with her, show her kindness and good treatment, and they are not permitted to shun her.

Sheikh al-Islam Ibn Taymiyyah was asked about a married woman who committed adultery. He replied that it is obligatory for her children and her male kin to prevent her from forbidden acts, and to confine or restrict her if she does not desist otherwise. It is not permissible for a child to strike his mother. As for showing her kindness, they are not to deny her their kindness, and it is not permissible for them to shun her. Rather, they should prevent her [from sin] according to their ability. If she needs sustenance and clothing, they should provide for her and clothe her. It is not permissible for them to carry out a hadd punishment on her, whether by killing or otherwise.

From this, it becomes clear that one of the greatest acts of kindness towards this mother is to work on protecting her and preventing her from committing indecency, so do not abandon her and keep her far from you.