I agree that ultimately it's their prerogative to have a child-free wedding, so long as they're gracious if this means some people can't attend (which it sounds like they will be).
However I understand completely that you'd be upset that your brother would rather you didn't attend his wedding, rather than make an exception for your kids. The absolute refusal to allow them in the vicinity seems very uncompromising and must be hurtful.
I don't think you should go and you should be clear why if your parents have the audacity to object. Your brother has made it very clear that the wedding is a child-free zone, even if this means you don't attend. They need to take it up with him if they have a problem (just make sure it's clear that you respect your brother's wishes, so any challenge your parents may make isn't attributed as having come from you).
We had a child-free wedding, but had any siblings had children they would have been the exception. Then again I know (or hope!) that we'll be very close to any future nieces and nephews, as we're close to siblings - it doesn't sound like you / your kids and your brother and his fiance have that relationship?
We also made an exception for breast-fed babies, as our intention in not inviting children wasn't to preclude their parents from attending! It was down to numbers and the kind of wedding we wanted - we hoped that everyone would be able to make arrangements with over 12 month's notice, and thankfully they did.