Is it permissible for me to cut ties with my mother and her family after they mocked my father and sided with my grandmother against me?

It is not permissible to sever ties with the grandmother and the uterine relatives on the mother's side. Severing kinship ties is one of the major prohibitions, and the grandmother is among the foremost relatives to be shown kindness. Their mistreatment does not justify severing ties with them. It is obligatory to maintain kinship ties and to repent to Allah for informing the mother about the grandmother's mistreatment of the father, as this is considered forbidden backbiting (namimah (definition)). Namimah is the disclosure of what one dislikes to be disclosed.