I’m going to assume that the bride is doing most of the wedding planning.
To her and your brother, you’re people who live the other side of the world from them. She’s only met you once, she doesn’t know you at all, her friends and family are all local.
Your brother hasn’t expressed his feelings about his family attendance enough or strongly enough.
You are low on the priority list for the bride. She’s throwing you a bone of names and numbers of random babysitters in this rural location, without thinking or caring too much about what that might mean for you. All of her local friends and family can sort themselves out via their own local networks.
I think you giving him an ultimatum of “kids come too or none of us come” will be the beginning of him feeling hard done by. He’ll take it out on you rather than his fiancée, because you’re far away and he doesn’t have to deal with you every day.
If you want this resolved, you have to frame this purely as a practical problem: you live 8000 miles away from us, we don’t know anyone or anything there, we will be very jet lagged, we don’t know our way around, no reasonable parent of a 4yo and a 1.5yo - children who can’t advocate for themselves, or speak full sentences frankly - would leave these children with strangers in a foreign country to attend an optional thing. This isn’t life-saving surgery, it’s a wedding. Thanks for inviting us two but we have to turn you down.
Keep your pissed-offness out of it. Make it his problem: he didn’t think it through, he’s ridiculous, what else did he think would happen?
What happens after that will be telling. But there it is.
Personally, this is breathtakingly selfish to me. They may as well tell you to your face they’re only inviting you out of duty, that they’re really only interested in their local friends and family.