She married the foreigner against her parents' wishes.
Literal
She [topic-は] parents [possessive-の] wish [to-に] defying that foreigner [with-と] married.
逆らう (さからう, 'to defy, go against') takes に for the thing defied. 願い (ねがい, 'wish') is the noun form of 願う. 外国人と結婚した uses と to mark the marriage partner. The sentence captures a classic family conflict narrative.