What should a husband do regarding his wife who refuses intimacy and touch, and prevents him from speaking with her brother after the brother saw them in an intimate situation?

Once a man formally contracts a marriage with a woman, she becomes his wife, and whatever is permissible for a husband with his wife becomes permissible for him. What you did is not haram, and there is no blame upon you for it, because you are her husband by virtue of the legitimate contract. It is preferable, however, to observe custom by delaying consummation. If you request that she be handed over to you after paying the advance of her dower, they must comply, unless there is a legitimate Islamic excuse preventing it. It appears that your private meeting with her causes them embarrassment, and this should be taken into consideration to avoid disputes at the beginning of married life.