I would put a note on the invitation that said something like:

DS has requested that his entire class comes to his birthday. As you can imagine this means a lot of children in our relatively small backyard. While parents are welcome to attend if they wish we ask that siblings do not attend due to area and catering restrictions.

Parents aren't going to stay if they can't bring the extra kids...

Maybe buy a couple of bags of lollypops of something and you can send siblings home with one if there are any party bag dramas.