We had that situation in our family a few years ago, Gillian, with cousins. The female cousin went, and left the child with her husband (who was happy enough to get out of it—after complaining, of course).

IMHO, the bride gets to make the final call on who does NOT come, but she does not get supreme power to determine who MUST come. IOW, the bride can veto kids, but can’t force parents.

I wrote a tongue-in-cheek (well, mostly 😉) take on the situation a few years ago:

Why Your Kid is Not Invited to Your Cousin’s Wedding