Hi Rachelle,
Most parents should know that when they get an invitation that is addressed to "one" of their children, it means only that child. They "should" inquire if it's ok that they bring siblings and if and when they do, you can let them know the cost of wherever your party is being held. And then just say "and of course they are more than welcome to have pizza, pop, cake and ice-cream".
Now for the parents who show up and bring siblings and just "expect" you to pay for everyone that's where you have to get your thick skin on and just plainly tell them that their other child(ren) are extra and they'll need to do that seperatly. And again of course they are included in the refreshments.
Your not the one being tacky by the way, it's the parents who assume or try and take advantage of the parents throwing the party that are tacky. So don't worry about it.
I just went to my god-daughters birthday party this past weekend at Build-A-Bear and my 4 year old son was invited but "not" my 9 month old daughter. So while the party was going on I built a lamb for my daughter and paid for it myself. And when my son went over his limit on the what each child was given to build an animal at build a bear, I gave my friend the extra money so it didn't come out of her pocket, as it shouldn't.
Or you could always have the parents just "drop" the kids off (hard at the pre-school age, but doable)then there is no way they can bring siblings. Just another thought.
Good Luck,
J. in Macomb