D.C.
You would hope that people are considerate enough to know that their other children are not automatically invited, but that's usually not the case.
I have 4 children very close in age. If one is asked to a party, I NEVER assume that the others are invited, nor do I 'invite' myself to bring them. I simply make arrangements for me to either stay with them without other siblings (when they were younger) or drop them off now that they are older.
Kids have to learn that they can't always do what their siblings are doing.
With that said, people unfortunately don't always think that way.. So my suggestion is as others have said ,,put it plainly on the invitation. Either 'invited children only',,, or siblings may attend, but must pay $x.xx extra per child. (of course, more nicely put than I said it, haha)
My 2 cents worth!