The decision to have children in or at your wedding always ends up a touchy subject. If not between the bride and groom than between guests and hosts. If you'd like to have children at your wedding, by all means invite them, if you choose not to be prepared for some guests who just do not understand why you don't want their little darlings racing across your dance floor and causing havoc. There is no hard and fast rule to include or not include children, it is the hosts' or bride and groom's decision.
It is not appropriate to add "Adults Only Reception" or "No Children Please" to your invitations. If you want to add it to somewhere put it on your wedding web site. The best way to handle guests who add uninvited children to their invitation is with a firm but insistent telephone call letting them know that you have a limited guest list and regret you cannot include additional guests. Also the mother of the bride or groom can simply spread the word among the family that it will be an adult party and express your regrets that you cannot include everyone's children.
You can provide a babysitter in a hotel room at your venue if you find it necessary. Check with local nanny services for bonded sitters or check with your hotel, most of them have sitter services on call.
