Is it obligatory to fulfill a vow to hit one's sister if she repeatedly commits certain actions, and is a light tap sufficient to fulfill the vow?

You are not permitted to hit your sister for the reasons mentioned. You must inform her guardian to undertake her discipline. This vow of yours is a vow of disobedience, and it is not permissible to fulfill it. It is safer to expiate for it with an oath expiation (kaffarat yamin). Advise your sister to fear Allah and to refrain from harming you.