My brother touched the hand of my uncle’s wife unintentionally as he was trying to hold my young cousin. Is he sinful? Am I sinful because I saw him and did not warn or advise him?

All perfect praise be to Allaah, the Lord of the worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and messenger.

If your brother intended to touch the hand of this woman, then he is sinful and he should repent, because he touched the hand of a woman who is a non-Mahram to him.

You should forbid the evil as much as you can and advise your brother. The Prophet, sallallaahu ‘alayhi wa sallam, told us that the essence of Islam is based on advising each other. [Muslim]

If you did not forbid the evil without having an excuse, such as forgetfulness or the like, then you are sinful because the Prophet ordered the one who sees an evil to change it physically with his hand if he is able to do so. If he could not, he should change it by his tongue (by advising and/or condemning), and finally by (detesting it with) his heart, and he informed that this is the weakest level of faith. [Muslim]