Inviting children to weddings is always a touchy topic, but if you decide that your guest list can not handle it, your venue may not be ideal, or you don't want the extra stress of adding methods to entertain children to your reception, you have every right to have an "Adult Only" wedding.
How do you make sure of this? If the names of the children are not on the invitation, then it symbolizes they are not invited. Some people do not know this, and some guests will pretend they did not notice the omission. There are a few other ways to make sure your guests are aware. The first way is with word of mouth. Start early by mentioning it to guests you talk to about the wedding and ask key people to help spread the word. Next, put a mention of it on your wedding website. It doesn’t hurt to offer a list of possible babysitters on the website as well for a further hint. Finally, it can be mentioned on the invitation itself with the reception card saying, “Adult Only Reception.” (And even if you decide on an Adult Only reception, you can always make an exception for your flower girl and ring bearer only.)
Bottom Line: If, after making it clear in various places, you are still concerned that you may have a guest who will bring a child, make it a point to call them and politely inform them of your wishes. If they get mad and tell you they are not coming, then it is their breach of etiquette - not yours.