I would not advise doing this.
It is poor etiquette to only invite some children and not others. Were you going to print up two sets of invites, one that says "adult reception" and another that doesn't specify.
In the long run it could cause some strain to your relationships with friends and family. Think of how you would feel if you were told not to bring your daughter somewhere, but when you got there, other kids were running around.
As far as driving numbers up, most kids don't really count as people, KWIM? One child will not eat and drink like an adult will. If you are having a hall/caterer they should base your rates on the number of kids & adults. So you want food for 125 adults and 30 kids.
If you will have a lot of kids, you might want to consider a Kid's food and activity table. Have PB&J sandwiches, fruits, goldfish crackers, etc. Have some small beachy toys, some coloring books etc. You might also want to hire a babysitter to oversee these activities.