Is a Kaffarat Yamin (expiation for breaking an oath) sufficient for my mother's vow to prepare a banquet for one of my teachers after my success, if fulfilling it becomes difficult?

This type of vow falls under the category of permissible vows, in which the one who made the vow has the choice to fulfill it or not. The more cautious approach, in case of non-fulfillment, is to offer expiation for an oath (kaffarat yamin). It is permissible for a mother to appoint her daughter to fulfill the vow on her behalf or to perform the expiation for the oath by feeding, clothing, or emancipating, but not by fasting, as proxy is not allowed in fasting because it is a physical act of worship. If the mother is deceased, it is recommended for her daughter to fulfill the vow or perform the expiation for the oath on her behalf.