What is the ruling on not communicating with abusive grandmothers and maternal aunts who have caused harm and slander, especially given the mother's inability to defend herself? And what is the maximum permissible period for not communicating with them to avoid severing ties of kinship?

If your mother did not receive her rightful inheritance, they must give it to her, and she has the right to take the matter to court. Boycotting the grandmother and aunts is not permissible, for they are like a mother, and maintaining ties with them is obligatory. The Prophet, peace and blessings be upon him, forbade shunning a Muslim for more than three nights, and the grandmother's ruling regarding filial piety is like that of a mother. Maintaining kinship ties should be done to the extent possible, as long as it does not harm the grandchild, such as by calling and inquiring about them, and enduring their mistreatment seeking Allah's pleasure, for that is among the greatest deeds that earn reward.