What is the ruling of Islamic law regarding dealing with a grandmother who expels and mistreats her son's children and his wife, and does not return their greetings?

The questioner is advised to be patient with the grandmother's mistreatment and to respond to it with kindness, for her right to dutifulness is not negated by her ill-treatment. They should seek help from Allah and supplicate for her guidance. As for the mother, she does not owe the grandmother the same degree of dutifulness. She should maintain good relations with her, and if the mistreatment persists and harms the mother, there is no sin upon her if she severs ties with her to the extent that removes the harm. Beautiful abandonment (hajr jameel) is to cease association without causing harm, insult, reproach, or complaint.