Is it permissible to give charity to the son of my deceased brother—who is under the care of his well-off mother—or is it more preferable to give it to a needy stranger?

It is permissible to give voluntary charity to a rich nephew, because voluntary charity may be given to those who are not in need. Giving charity to a relative combines charity and maintaining kinship ties, and this is better than giving charity to others, even if giving charity to the needy is better. As for zakat (definition), it is only given to those who are eligible for it, such as the poor, the needy, and those mentioned with them in the verse of zakat.