Is it permissible for a woman to travel with her eight-year-old son and her daughter who is of age only?

A woman is not permitted to travel without a mahram, due to the Prophet’s (peace and blessings be upon him) saying: "It is not lawful for a Muslim woman to travel for a night's journey unless a dhū ḥurmah (a male relative within the prohibited degrees of marriage) is with her." A young boy, like an eight-year-old, is not considered a mahram. The condition for a mahram is that he must be an adult of sound mind, capable of protecting the woman. Therefore, it is not permissible for a woman to travel with her eight-year-old son.