Will a father be held accountable for his children's disobedience due to his revealing of his marital and private problems everywhere, which embarrasses them, and for his lack of tenderness and mercy towards them and his preference for himself in everything? And are the children sinful in this?

The father has a great right over his child to be dutiful to him and to treat him kindly. Among the greatest acts of dutifulness is to advise him gently and kindly if he errs, to seek help from someone who influences him, or to seek help from Allah to rectify his affairs, especially if what he is doing is significant, based on the Prophet's (peace and blessings be upon him) saying: "Indeed, among the worst people in rank before Allah on the Day of Resurrection is a man who goes to his wife and she goes to him, then he divulges her secret." If the father causes harm to his children, he is held accountable for that. He must spend on his young children, and the children have no right to object to his spending on himself as long as it is not outside what is permissible. The wording "Help your children so they may be dutiful to you" has not been authentically narrated as a prophetic saying (marfu'), but Ibn Hibban narrated from Ali (may Allah be pleased with him) that the Messenger of Allah (peace and blessings be upon him) said: "May Allah have mercy on a child who helps his child to be dutiful to him." Its meaning is sound: that fathers should be a help to their children in their dutifulness. Nevertheless, it is not permissible to be undutiful to a father, even if he does not fulfill his duties.