I wish there was a directory for Jean Bean's school. I don't even know for sure how many children are in her class yet; class pictures were only just taken and won't come home for another ~3 weeks. There is a rule about inviting "all" kids in class, but I told her we are doing a Family Only party this year, and she can get phone numbers herself next year; we're bringing cookies to class on her birthday (teacher approved) so she has her special moment amongst her peers.
We had similar experiences as described in the OP. A couple years ago, we invited a little girl (very loosely related) to Jean's birthday. Her mom, dad, older brother all showed up. After doing the craft and handing out goodies, the little girl asked me when I would be handing out gifts to the guests "to make it even." I explained it was only the birthday girl's birthday, but we'd given her craft + accessory. "Is that all?" the child whined. Her mother stood by and said nothing.
Some time later we were invited to a family/ friends party for the older brother of the Gimme Child. We gave him a gift of a two person playset. The mother came over to my husband and me and said something along the lines of (sorry, it's been a while but I'll try to remember exact wording) "You know, when you give one of my kids a gift, it's a lot easier to give a gift to each. It's just how my kids are."
She was aggrieved some time later to discover I had unfriended her on Facebook. We may be loosely related but that doesn't mean I have to pay her kids to come to my daughter's birthday parties, or pay for the privilege of going to theirs.