All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
We ask Allah to enable you to do good.
You should object to your mother – in a gentle and soft manner – and explain to her the seriousness of backbiting and its bad consequences.
If she does not take heed and stop backbiting, then it is not permissible for you to sit with her in this case, unless she stops backbiting.
If there is any necessity that prevents you from leaving the gathering, then it is permissible for you to sit but do not listen to backbiting and occupy yourself with the remembrance of Allah and the like.
The fact that your mother is feeling resentment at your denial or when you leave the gathering, then this does not allow you to tale part in the backbiting meeting.
In his Book Kitaab al-Athkaar, Imam An-Nawawi detailed what is obligatory for a person to do when he hears someone else backbiting people, and he said:
“Know that (regarding) backbiting – just as it is forbidden for the backbiter to say it – (it) is also forbidden for the listener to listen to it and approve of it. Therefore, it is an obligation on someone who hears a person starting prohibited backbiting to forbid him from doing so if he does not fear an apparent harm. If he fears an apparent harm, he should deny it in his heart and leave that gathering if he is able to do so. If he is able to deny it with his tongue or to interrupt and divert the backbiting by saying something else, then he is obliged to do so. If he does not do so, he is disobedient (to Allah). If he is obliged to remain in that meeting where there is backbiting and he is unable to deny it, or that he objected to it but people did not accept to listen to him, and he was unable to leave in any way, then it is forbidden for him to listen to the backbiting. In this case, he should mention Allah with his tongue and his heart, or with his heart only, or he should think about something else so that he would busy himself from listening to the backbiting. If he becomes able to leave after that while they are still continuing in backbiting and the like, then he is obliged to leave. Allah Says (what means): {And when you see those who engage in [offensive] discourse concerning Our verses, then turn away from them until they enter into another conversation. And if Satan should cause you to forget, then do not remain after the reminder with the wrongdoing people.} [Quran 6:68] [End of quote]
For more benefit on when backbiting is permitted, please refer to Fatwa 82663.
For more benefit on failing to denounce backbiting out of shyness, please refer to Fatawa 343228 and 342127.
Allah knows best.