What is the solution for dealing with a mother who is characterized by extreme nervousness, backbiting, causing family disintegration, interfering in personal life which led to two divorces, inciting the daughter and depriving her of her mother, in addition to slandering and questioning morals and being hostile to religion, knowing that her daughter is suffering psychologically because of her?

The ill-temper of parents and their distance from religion do not justify disobedience to them. A child must honor them and treat them kindly. What you mentioned about your mother does not justify cutting ties with her or treating her badly. The mother's right is greater and more emphasized, but you have the right to request the return of your daughter from her. What your siblings did by cutting ties with your mother is a great mistake, and they must repent from it. You and your siblings should advise her gently and strive to supplicate for her guidance. Seek help from those who can influence her. It is possible to avoid the harms of her company through wisdom and gentle persuasion. If you treat her well and are keen on advising and guiding her, that will bring good to you.