Hi C.,
Firstly, you did not mention 'no gifts', so everyone assumed you wanted them. Secondly, are you saying the adults should pay for theirs, and you will take care of the kiddies; or, do you disavow yourself entirely?
Either way, it's about as tacky as it gets. Inviting and then informing them they have to pay to play is such bad form. Would you want them to tell their kids that they can't go to your party because they can't afford it?
Proper etiquette dictates that you make the guests feel special. I wouldn't feel that going to your party. You are obliged to pay the entire cost.
How about another alternative like fewer guests. Balloons, ice cream and cake is all you need; a few little finger foods around, hot dogs. Remember, the Dollar General is a good source for many party items and delicious munchies; as well as little grab bag gifts to distribute to the kiddies as they leave, etc.
That shows a caring host. It could be done in your backyard. Nice and simple. That being said, would you still expect the invited guests to pay when they arrive? lt is no different for a wedding, you do not invite, then make guests pay for their meal and drinks. All the best.