What is the Sharia ruling regarding a husband preventing his wife from visiting her family, especially after he has sworn to it, due to his suspicion about the conduct of her brother and his wife, and is he permitted to prevent her from visiting them while he is aware of her brother's frequent visits to his family?

We do not know the nature of the oath you swore. If it was an oath by Allah, then you may expiate for it and allow your wife to visit her brother, as long as you do not fear any corruption for her, due to the saying of the Prophet (peace be upon him): "Whoever swears an oath and then sees something better than it, let him expiate for his oath and do that which is better." However, if it was an oath of divorce, then divorce occurs upon her visit to her brother's house according to the majority of scholars. While Sheikh al-Islam Ibn Taymiyyah held the view that if the oath was intended for prevention and threat, then it does not necessitate divorce but rather an expiation for an oath.