Is an oath valid for someone who swore on the Mus'haf to divorce his wife if he saw his brother's wife in his parents' home, knowing that he swore to cut short problems in front of his children?

If you looked at your brother's wife in your parents' house, then your wife is divorced based on the suspension of divorce upon your looking at her and your swearing by the Qur'an. This is the view of the majority of scholars. If the divorce occurred and it was not the third divorce, then you may take back your wife during her iddah (waiting period). Some scholars hold the view that the ruling on swearing by divorce, when the intention is not to suspend divorce but rather to threaten, is the same as swearing by Allah. Thus, if the oath is broken, the one who swore it must pay an expiation for an oath, and no divorce occurs. A man may use tawriyah (double entendre) and tarid (allusion) in his oath if his wife asks him to swear by her divorce.