Is my understanding correct that a grandfather's maintenance of his son is not obligatory because the son has an income, and a father's maintenance of his brother is not obligatory because the brother has an income, and a father's maintenance of his wife and children is not obligatory because the father has an income, even if he is poor?

The majority of jurists hold that a father is not obligated to provide for his adult son who is capable of earning a living. Therefore, your grandfather is not obligated to support your poor father, nor is your father obligated to support your adult brother who is capable of earning a living. The Hanbalis are of the view that the maintenance of a man's wife is incumbent upon whoever is responsible for his maintenance, unless he is able to provide for her himself. Compassion and mutual support should prevail among members of the Muslim community, especially among relatives.