Should we invite children to the wedding?

What are your guys' thoughts on children being invited to weddings? I've heard that some adults like the chance to get away from their kids, and some feel offended by not being able to bring their kids.
The thing is, we are paying 50 bucks a head for the caterer, and it is an evening wedding that will be going until late- not the most kid friendly event. Our families have very few children in them, but our family friends and old mentors, etc. have around 35 kids altogether. So these kids are not related to us or anything- and we never see them or think twice about them. But we want their parents to be there, and the wedding is out of town (about 2 hours from where we and most of our guests live), so I worry that if we don't invite their kids they won't come, or will feel slighted.
I was considering hiring a sitter for them, but with that many kids I'm worried it will be an absolute zoo... Should we just buck up and pay for the kids to come, or would it be ok to not invite them?
Thanks for any advice!