Is it permissible for my fiancée to break her fast while she is making up (for missed fasts) because you have a sexual need for her, knowing that you have already solemnized your marriage contract?

A make-up fast (Saum al-Qada') may not be broken once started without a valid excuse. The correct view is that a husband does not have the right to order his wife to break her fast if she is making up a missed fast without his permission, and she must complete her obligatory fast.