Actually, without dispensation from the bishop, the marriage would not be valid in the eyes of the Church; it is not about the Orthodox having “valid sacraments,” because according to the Catholic Church, the husband and wife are the ministers of the Sacrament of Matrimony, not the priest. So that the Eastern Churches have valid orders does not matter. According to Canon Law, marriages must be witnessed by someone expressly delegated by the Local Ordinary (Bishop)
Canon 1108.1 Only those marriages are valid which are contracted in the presence of the local Ordinary or parish priest or of the priest or deacon delegated by either of them, who, in the presence of two witnesses, assists, in accordance however with the rules set out in the following canons, and without prejudice to the exceptions mentioned in cann. 144, 1112.1, 1116 and 1127.2-3.
Canon 1115 Marriages are to be celebrated in the parish in which either of the contracting parties has a domicile or a quasi-domicile or a month’s residence or, if there is question of vagi, in the parish in which they are actually residing. With the permission of the proper Ordinary or the proper parish priest, marriages may be celebrated elsewhere.
Getting married in the Catholic Church, provided you have dispensation from your Bishop for Disparity of Cult (marrying a non-Catholic) WOULD NOT place your fiance in an objectively invalid marriage. Her Church may say her marriage is invalid, but that does not mean they are correct. The Catholic Church is the fullness of the Church, not the Eastern Churches - let’s not place them on the same plane.