I've run into that sort of thing several times and each time, it pisses me off even more.
In your case, I would probably write a letter outlining the incident and cc it to the local Chik Fil A as well as the district manager and corporate headquarters. I don't think people should get away with that nor do I think people who are simply doing their job should be reprimanded for it.
That said, I usually handle situations like that by asking the child in question their name, then once I get that, I loudly ask them, SANTO, WHERE IS YOUR MAMA? Either the child points them out or the mother speaks up, then I talk directly to them. It may not have made a difference in their behavior or the outcome, who knows?
As a mother whose children have large age differences, 7 years between the first two and 10 between the second, the older ones always want to play and climb in those playgrounds with the younger one. I allow it with two provisions: there are no other small children in the play yard and they must leave if any other small children arrive.
Anyway, I can't stand parents who think their children can do no wrong. Hey, your kid bonks my kid upside the head with a cedar block, you bet your going to hear from me. If one of mine shoves one of yours, they will apologise and sit in time out until they think they can play nicely.
Just my 2 mins of babble
Stormie