Is it permissible for a mother to rub her son's back in the bathroom while his minor 'awrah is uncovered?

A man's 'awrah is from the navel to the knee. He must cover it from people except for his wife or female slave, based on the Prophet's (peace and blessings be upon him) saying: "Guard your 'awrah except from your wife or what your right hand possesses," and his saying: "Cover your thigh, for the thigh is 'awrah." Therefore, it is not permissible for a mother to look at or touch her son's 'awrah unless he is a young child.