People have NO concept of good manners these days (sorry if I offend anyone). When an invitation is received, only the person to whom it was addressed is invited. When my husband and I received a wedding invitation this summer and it was addressed to "Mr. & Mrs. P . . .", we understood that our daughter was not invited. No questions asked. My daughter is an only child, however, I would never assume a sibling was welcome unless the invitation was addressed to more than one person.
I have had several parties for my daughter out in a place where you pay for each child. I've also done parties at home (elaborate tea party, for ex, where an older sibling not only ruined the party by having an attitide, but there was nowhere for her to squeeze in at the dining room table I had spent days preparing).
You absolutely can write on the invitation "no siblings, please". When you get the RSVP call (which nobody has the courtesy to do anymore either), make sure you say - OK, so I'll mark Sue off as ONE). If you think that they still believe the sibling can come, say - oh, I'd love to have little Mikey, but I'm afraid we won't be able to accommodate him. If they say that they won't be able to come unless the little one can come (which so many people do), simply say - Oh, I'm sorry, we'll really miss little Sue at the party. Stick to your guns. The same people who overstep their boundries by bringing the sibling are the same people who have never paid for a party in a venue. Off my soapbox now.