Send the invitation in the childs name only...The invite should read the location, date and hour of the party along with an RSVP phone number. If you are going to make arrangements to have these children driven to and from the party...also add that information in the invitation along with the name of the driver and the pick up and delivery time. (((If you want to be at your party earlier to greet your guests, that time will be different then the time of the actual starting time of the party...unless someone else then you is going to be doing the driving.)))) And because you are making special arrangements for children, be sure you follow this up with a phone call to their parents a week before the party so everyone is on the same planet and there are no misunderstandings...
I can understand that you want to keep the guest list small. But I can't understand why you want to take on the responsibility of these other children on a day that is going to be hectic for you. Inviting these children without a parent means you will have to supervise these children properly at all times. For them it means going to a party...in general it's going to be an adult party...not exactly a play day for them.. Unless you are going to provide one adult to supervise these children at the party...This wont leave you much time to enjoy your party and your other guests. I tend to think you need to re-think what you are willing to take on...
As for your #2 reason that families don't know each other....I don't see this as a problem. At parties, people meet and mengle with each other even if they have never met before. They are all there for a common cause of celibrating your childs communion and having a good time...