Another family member cheerfully said in response to the situation: "this is what they signed up for when they decided to get married at such short notice! It's a shame not everyone will be able to make it."
I've fixed the above quote for you so that it makes more sense.
I'm glad everyone else called out this manipulative BS for what it is. My family used to do that same stuff to me - Aunt such and such can't stand to be in the same room with Cousing so and so , meaning that you'll have to organize two different visits....
On a practical level, I don't think it's unreasonable at all for the bride and groom to slip you a few hundred dollars towards the ticket without telling anyone. They'll be flushing plenty of money down the toilet anyway, probably spending £500 on the little tissue inserts on the invitations so they should just consider it another wedding cost.
Another alternative is just to fly yourself over one day before the wedding and leave one day after. Then all the attention will be on you, super effective passive aggressive get back on the bride.