How can one deal with a mother who frequently backbites without angering her, knowing that attempting to defend those being backbitten provokes her anger and she may sometimes be in the right? Is silence in this case considered listening to backbiting? And does backbiting nullify a mother's good deeds, such as fasting, prayer, and charity?

Backbiting is forbidden, and it is one of the major sins. Listening to it is also forbidden and makes the listener a partner to the backbiter unless he stops him. One must repent to Allah and cease listening to backbiting, and gently admonish the mother by disapproving of it and explaining the ruling of the Sharia (definition), and engage her in conversations that benefit her religiously and worldly. If she sees your persistence in disapproval, she will, Allah willing, stop backbiting.