Is the mother considered sinful or at fault for convincing her daughter to stay with her mentally ill husband, from whom she had suffered physical abuse and humiliation, and due to whom she and her children are still living under psychological pressure, especially after the father initially rejected the idea?

The mother does not sin by striving to preserve her daughter's family and by enjoining her to be patient with her husband, especially for the sake of the children. Muslims are commanded to be patient, and this is especially true for spouses, as repelling evil with good transforms an enemy into a close friend. Perhaps her patience has borne fruit in the improvement of his condition, and her continued patience will increase that. The man should be advised to fear Allah and to improve his treatment of his wife, for injustice to her is darkness that Allah hastens to punish its perpetrator in this world, along with what He has stored for him in the Hereafter.