The Biblical Father is called

Intercedes for his family and represents them before God

Represents God to his family thru spiritual education and instruction

Governs or rules his family/household on behalf of God

Lot offered his two daughters to the evil men who were wishing to have sex with the two angels/men in his home. His daughters got him drunk and had relations with him fearing they would not bear children. Lot was partly responsible for this

Isaac married a deceptive wife named Rebekah and favored his son Esau which made him spoiled and foolish while failing to offer guidance to his other son Jacob. In the end, Jacob and his mother plotted and tricked Isaac, thus stealing his brother Esau's inheritance

The Bible calls King David a man after God's own heart twice, yet he was an absentee and passive father, who spent more time on the battlefield than with his family. David commits adultery with Bathsheba impregnating her, and when he couldn't cover it up, he had her husband Uriah murdered in battle