Kids are adorable and hilarious, but that does not mean you have to have them at your event. There are polite ways to indicate on your invitation that you are hosting a kid free event. Beyond these options, you can also write the names of the invited guests only - Jane and John Smith for example. Another option is to write in the number of guests for them on the rsvp card, put that 2 on there for them, so that it is clear exactly how many guests are invited.
The kid question is often going to be controversial. Some people insist on bring them (babysitters are expensive) and some parents really want to be with you but still have children dependent on their mothers. Allowances have to be made at times and that might ruffle some feathers. Remember this is your day and you should do it your way, however if it is important that someone is there with you, you may need to make sure to meet their needs. You can always offer to have a babysitter in another room or be understanding about kids being at the ceremony but taken home for the reception. Flexibility will go a long way in appeasing your guests.