How can this family live a happy life in light of the husband's favoritism toward his family, his children's hatred of him, and his neglect of his wife and children?

What a husband does in terms of shortcomings towards his wife and children is an injustice and a dereliction of what Allah has obligated upon him. He is responsible for his flock, and taking care of one's wife and children is akin to jihad and charity. It is not permissible for him to neglect their rights under the pretext of caring for his family, for everyone has rights. The wife should be patient with her husband, advise her son regarding prayer, and supplicate for him. The husband's preference for his family is not an injustice if he fulfills his financial obligations towards his wife and young child.