Is it permissible for me to perform Hajj on behalf of my deceased father or my deceased mother, after I have performed my obligatory Hajj, knowing that my mother was more diligent in prayer and more pious than my father?

If your father passed away and a mandatory Hajj was incumbent upon him, perform Hajj on his behalf, unless your mother is in a similar situation. Otherwise, your mother's right takes precedence over your father's right, due to the Prophet's (peace be upon him) saying: "Your mother, then your mother, then your mother, then your father."