Is it necessary to seek forgiveness or to rectify past wrongs through good treatment after things have returned to normal between the parties, especially after sincere repentance?

If no aggression or injustice was committed by you against your brother or his wife without right, then nothing is incumbent upon you, and there is no sin upon you if your brother leaves in anger due to your admonishment of his wife for her slander. You are obligated to maintain ties with him in a good manner. However, if aggression or injustice was committed by you without right, then your repentance is to apologize to them both and ask for forgiveness.