When a couple decide not to invite children to their wedding (or decide to invite only some of them), they can head off drama (and kids) by getting the word out, informally, before the invitations are sent.
I used to suggest that they call the family matriarchs and ask them to spread the word -- partly to borrow their authority, and partly because sometimes Grandma is the one who cares.
But I have to change that advice. Lately, I've run into several people who were offended at not being given that news directly, from the bride herself. They felt "fobbed off" and maybe even a bit manipulated. It felt dismissive and impersonal.
I still think you should include the matriarchs in the phone calls, but now I'd say, go first to the parents of the children you won't be inviting. Tell them you're having to make some difficult decisions about your guest list, and that you won't be inviting any children to the event (or will be inviting only those kids most closely connected to you, if that's your decision).
Say you're sorry not to be able to include their children (compliment the kids, if you can -- that always makes parents feel better), and that you're calling early to give them as much notice as they can to find a sitter. And then also say, "We'll certainly understand if you aren't able to attend, but we're hoping that you'll recognize our situation and share the day with us."
Will you have to make phone calls like this -- or have you done so already? How are you alerting people to the restrictions on your guest list?