Is it permissible to give Zakat al-Mal (obligatory charity on wealth) to a nephew who is a child living with his divorced mother, knowing that the father is unemployed and the mother and grandmother are spending on him and on their grandson?

If your nephew's mother is wealthy and able to spend on him, then it is not permissible to give him zakat. However, if she is poor and your brother is unable to spend, then it is permissible to give him from zakat, and he is more deserving than others.