Is it permissible for the husband to refuse further childbearing, despite his wife's desire for it, due to her mistreatment of their first child and the fear of a repeat of the situation?

The Shari'ah permits disciplining a child who understands the purpose of discipline. Part of this discipline is striking, if other methods are not effective, based on the Prophet's (peace be upon him) saying: "Order your children to pray when they are seven years old, and strike them for it when they are ten, and separate them in beds."