Is it permissible to inform one's mother about a situation involving discriminatory treatment between siblings, so that the mother may advise the son on the matter, or would that be considered backbiting and calumny?

If there is no apparent benefit in informing your mother about what happened with your relative, then do not tell her. However, if there is a benefit in informing her, such as consulting her and seeking her advice on how to deal with him, then there is no objection. The principle is to think well of Muslims and to interpret their words and actions in the best possible way, as Umar ibn al-Khattab, may Allah be pleased with him, said: "Do not think ill of a word that comes out of a Muslim's mouth if you can find a good interpretation for it."