Is it permissible for a mother to continue mentioning the faults of her siblings and relatives and what she has suffered from them under the pretext of "venting," while knowing that this falls under the category of backbiting, and what is the optimal way to deal with her?

The basic principle is the prohibition of mentioning a Muslim with what he dislikes in his absence, and this is one of the major sins. An exception to this is the mention by the oppressed of his oppressor by way of retribution, such as for the purpose of repelling injustice or exacting a right, or by way of retribution without aggression or falsehood. Abstaining from that is more preferable and better.