Is an expiation for an oath (kaffarat yamin) sufficient for fulfilling a vow to hold an Islamic wedding, especially if the parents refuse and threaten not to attend?

If by "Islamic wedding" you mean a wedding free from forbidden acts, then it should be so even if you did not vow it. A vow to perform an obligation or to abstain from a forbidden act is not binding according to the majority of scholars. So, if the one who made the vow does not fulfill it, no expiation is required of her. What is obligatory upon her is repentance from abandoning an obligation or committing a forbidden act. Your vow is not binding, and you must avoid disobeying Allah in the wedding and not establish or permit reprehensible acts, for there is no obedience to a creature in disobeying the Creator. If your parents do not respond, then hold your wedding in obedience to Allah, and there is no sin upon you if they do not attend.