Can you invite some kids to your wedding, but not others?
This is a tricky question. Technically, it’s your wedding and you can invite whomever you want. If you want to invite your nieces and nephews, but not your friends’ kids, you’re allowed to do that. If you want to invite all kids except a few because they're annoying, you’re allowed to do that too. Just address the invitations to exactly who is invited.
I would recommend that it is more polite to have an across-the-board policy regarding kids. It may be possible to have the policy be “only immediate family members” or “only nieces and nephews” or even “only kids coming in with parents from out of town.” However, if this policy is not clear to guests who had to leave the kids at home and find a babysitter, they might wonder why they couldn’t just bring their kids if so-and-so did.
The easiest way to handle the kids situation is to just invite all of them or none of them. If it’s not going to ruin your wedding to have certain children there, it shouldn’t be that much different to allow other kids as well. And, you avoid any risk that parents may be offended, or think that you just don’t like their kids.
Of course, it is equally as acceptable not to invite any kids, especially at formal, evening receptions.
This is a question that is very situation-specific, and you should use your best judgement. Remember that any etiquette guidelines are meant to make others feel more comfortable and at-ease, so that should be the guiding principle in any etiquette-based decisions you make.