I don't think it is rude at all specially at a wedding. You're paying $100 a plate. Most places don't give you a break for kids. so unless that parent is going to increase thier gift by a like amount, I find it very rude of them. When invitations go out it should specify adults only or address it to "and family" either way. But if you are specifying no kids, your kids should not be there either unless it is like a wedding where there is an assigned cost.
Yes, we all agree that the cousin was very rude to ignore the specific request to leave kids at home. BUT, I still think it's equally rude to exclude relatives due to their young age. It's treating them as expendable strangers. Most uncivilised, I think. A very Western anti-family chilliness and hubris there. Let's hope those who exclude the small children of family members from social events, don't one day need those same kids to take care of them in some way. "I couldn't tolerate you at my two hour party, but please come and change my adult diapers for the next three years til I die".
People have different ideas about weddings. Some are happy with a backyard BBQ and others prefer a little more formality and good food and wine.
We went for the happy compromise. VERY good food, no wine (no alcohol, period), and 'backyard'. Helps to know excellent cooks from the mother country, who fall over themselves to cater weddings in the community
It was fun (for the guests, not the hard-working bride and groom, so much .. but that's what honeymoons are for!), and tasty. But fear not, probably only 10 of that 40 were actually drinkers, so most guests wouldn't have registered that there wasn't any.
Private property, or rented as such, and private event. Yes they should be able to do so and suffer or benefit accordingly.