Is it permissible to dispose of the grandmother's entrusted money after she has relinquished it to the inquirer's mother for the purpose of spending on his younger brother? And is it permissible to withhold the money until the brother reaches maturity, under the pretext of the trusteeship and the mother's excessive spending?

An agent is not permitted to violate the instructions of their principal. Any violation is considered a breach of trust. Your grandmother did not give you an absolute power of attorney; rather, she authorized you to receive her share and give it to your mother to spend on your younger brother. Therefore, you are not permitted to dispose of the money in a way that contradicts this general authorization. Your obligation is to hand over the money to your mother for spending on your brother.