Grays - my girls would also be "devastated" if we went to a wedding they weren't invited to. They are 8 and 10 and have barely ever been to a wedding in their lives because either they weren't invited, or the wedding was abroad or similar. They love dressing up (they have loads of lovely dresses they get no opportunity to wear as most kids parties seem to be at soft play or wildlife parks), and they love dancing, so why wouldn't they love a wedding? Plus they love looking at grownups wearing lovely dresses etc.
Personally I don't consider a wedding "an adult affair", I consider it a family affair and part of the charm (IMHO) is that a spread of generations are there. When people say they couldn't invite kids as it would raise the numbers and mean they couldn't invite other people, I'm sceptical. Apart from the scenario of an actual maximum headcount for a venue, it actually wouldn't cost much to invite kids, surely any venue or caterer worth its salt could provide a kids meal eg pasta or chicken and chips pretty cheaply and a LOT cheaper than an adult meal, plus they are not drinking wine are they?
Admittedly when I got married I didn't know loads of people with kids, but we had cousins, and some friends' kids there. Apart from the very small ones who sat with their parents, we had a kids table so they all sat together and entertained each other (next door to the parents' tables so they could keep an eye) One of my favourite pictures/memories of the evening is my young cousin who was a bridesmaid twirling round with her skirt flying out.
As far as disturbing the ceremony is concerned, if you're not convinced the parents have enough sense to do this anyway, you could have a word beforehand, asking them to take a young child outside if they become noisy or disruptive. (Our head teacher says the same at the beginning of school plays) Most parents would surely do this anyway. There is no way I would sit there with my child screaming in a ceremony.