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I would be as completely appalled and non-supportive of this so-called marriage as the LW. But given that her husband is going regardless, and that her daughter feels such a camaraderie to her young cousin, I would go simply for the shared family experience. You don't have to support this union in your heart. Hell, most marriages end in divorces anyway. I don't give this couple 2 years before it's splitsville. Just go and be a good sport- take one for the team. You can be a good example for your daughter in that way.
And as many have already pointed out, don't worry about your daughter wanting to run off and get married just because her dorky old-world fundamentalist christian cousin did. Most kids are way too hip and precocious for that kind of retrogression. At this point, you just have to trust that your daughter has enough good sense, because you have given her good guidance during her formative years. A guidance must have been worlds apart from the guidance her cousin received.