What is the Islamic legal ruling regarding dealing with a wife who repeatedly leaves the home without permission, and demands separation because there is another person in her life, and how should one act concerning this, while considering the injunctions of Allah and His Messenger concerning the mother?

The husband must oblige his wife to fulfill the rights of Allah Almighty and his own rights, and prevent her from mixing with non-mahram men. The husband should explain to his wife the obligation of obeying him and not leaving her home except with his permission, and the impermissibility of seeking divorce without cause. If the wife repents and returns, the husband should keep her. Otherwise, he may refrain from divorcing her until she waives some or all of his rights. Her separation becomes recommended or obligatory if she neglects the rights of Allah. Regardless of the mother's situation, children must honor her and obey her in what is good.