In the case described:
- dispensation from the Catholic canonical form of marriage is only required for lawfulness on the basis of canon 1127 §1: The prescriptions of can. 1108 are to be observed concerning the form to be employed in a mixed marriage; if a Catholic party contracts marriage with a non-Catholic of an oriental rite, the canonical form of celebration is to be observed only for liceity. . . and
- the required permission in canon for mixed religion in canon 1124 (i.e., to a baptized non Catholic) pertains to lawfulness rather than validity. Even though that canon uses the term “forbidden,” it does not impose the burden of invalidity. This is different from the impediment of disparity of cult in canon 1086 (marriage to the unbaptized), and is not itself listed among the diriment impediments.
If the Catholic manifested an intention, despite the required prenuptial promises, to raise the children Orthodox, I should think the local ordinary might withhold both the permission and the dispensation. Without them, the marriage would then be celebrated validly on the basis of those canons, but unlawfully.