when really, you have no idea who made up the rule - the mother could have just been the messenger
Being passive aggressive and playing oh-so-nice at school and then cheerfully waving good bye to the girl she told her mom not to invite?? If that seriously was what happened? I'd leave the school and never go near there for fear of screaming at a child. And I certainly wouldn't want my kid anywhere near that child for fear of the child becoming worse and worse with age.
And as a mother, if my kid decided she didn't want to invite a kid who'd been to the party the previous year, I'd find out why, and I'd do what I could to help her work out the issue.