I don't think it's reasonable for people covering the costs of a wedding to be expected to pay for surprise extra guests. Presumably DD and BF weren't even together when the initial plans were made and invitations sent. It's a young relationship, and weddings are expensive and complicated.
She is acting like a typical teenager muddle of child and adult. On the one hand, as a child, she wants things to be paid for her. (If she were 30 at the time of her father's remarriage, presumably she wouldn't expect him to cover her travel costs - so this is a child-based expectation.) On the other, as an adult, she wants her relationship to be treated as a central and essential part of her life, not seeing, from her youthful perspective, that it's really only quite a short relationship, and without having the experience of being partnered and getting wedding invites that will eventually teach her that partners are very often not invited to weddings - definitely not if the relationship didn't exist when the wedding was planned, and even often if it did, as space is always tight.
It's very teenage to be joined at the hip in a relationship. That isn't to put down her feelings, teenagerdom is an important and complex stage we all go through. But ultimately I don't see why they should cover the costs for a latter-minute guest who is a boyfriend of a few months.
I wonder what else is going on here. Why is she so adamant she won't go without him? Is she nervous or worried about the wedding and feeling lost among her dad's new life that she doesn't feel secure in?
In your position, honestly, I would probably pay myself for DD and BF, as that seems the simplest route to making her happy!