What should children do with their mother who insists on visiting shrines whenever her illness worsens, and they observe her condition improving after the visit, while they cannot disobey her for fear of her crying and accusing them of negligence?

It is not permissible to obey one's mother if she asks to visit shrines seeking healing, because that is shirk (polytheism) and assisting in sin. Allah Almighty says: (And do not cooperate in sin and aggression). The Prophet, peace and blessings be upon him, said: "There is no obedience to a creature in disobedience to the Creator." It is obligatory to teach her gently and wisely that what she seeks is forbidden by Islamic law, and that these deceased individuals possess no power to harm or benefit themselves. Her feeling of improvement after the visit is a deception or an illusion from Satan.