Same here. My kids are never more than an arm’s length away from a grown-up, basically. This past Easter, though, we went to a buffet with my in-laws. I did allow my kids to be off with their older (14 and 16-year-old) cousins, but that was pretty twitchy for me. I kept thinking that I should be nearby, ready to sternly glare and drag one of them off by the ear if they got rowdy. But I know that the cousins would not put up with any rowdiness.
Honestly, it seems that the parents described in the OP were dicks first, (ineffective) parents second. Who fails to notice a conversation between the waitress and the patron behind them about who can I speak to about this disruption, is there another booth I can sit in, etc?
ETA:** Lurker**, it sounds like the manager was a dick, too. No one felt like acknowledging your spilled coffee, for instance?