Are the children sinful for not informing their mother, who is diabetic, of the truth about the amputation of her inflamed toe, and for making her believe that it is a normal operation for her own good? And what is the expiation for that?

Surgery is not permissible for a patient except with their permission, if they are an adult, of sound mind, capable of granting permission, and their health condition allows it. This has been affirmed by the Islamic Fiqh Academy and emphasized by jurists and doctors. Evidence for this includes: Aisha (may Allah be pleased with her) said: "We gave medicine to the Messenger of Allah (peace be upon him) in his illness, and he signaled to us: 'Do not give me medicine forcefully.' We said: 'It is a patient's dislike for medicine.' When he recovered, he said: 'Did I not forbid you from giving me medicine forcefully? No one in the house shall remain except he is given medicine forcefully, while I watch, except for Al-Abbas, for he was not present with you.'" Therefore, it is not permissible to lie to the patient or perform surgery without her permission. Rather, her consent must be obtained, and one must seek forgiveness and pardon from her.