Are the children who secretly meet their divorced mother and send her food, without their father's knowledge, and who invokes Allah's displeasure upon them for it, sinful, knowing that Allah has commanded obedience to parents?

Your father does not have the right to prevent you from visiting your mother, and there is no obedience to him in that. Visiting her without his knowledge is not a sin; rather, you will be rewarded for it. His cursing you and his displeasure with that will not harm you. However, taking food from your father without his permission to give to your mother is not permissible, due to the saying of the Messenger of Allah (peace be upon him): "The wealth of a person is not lawful except with his willing consent."