Send paper invitations, and address the invitation to each child you are inviting.
Larla Smith
or
Brayden and Jayden Jones
If a kid's name isn't on the invitation, he/she isn't invited. The real problem is that some parents will bring siblings who aren't invited. Saying "no siblings" seems rude, but it's only necessary because (rude) people presume to bring uninvited guests. They may be less likely to do this, however, if the invitations are addressed to specific kids.