The famous "skillet" you're referring to, would that be the skillet at the Whispering Canyon Cafe?
The Garden Grille brings out chicken fingers, fries and mac & cheese as part of the family-style meal, we didn't have to ask for it for our kids.
The meal is all you care to enjoy. My boys just had to dine there twice on our last visit. On our second visit, we asked for more steak served well-done, no catfish and two bowls of salad. The server couldn't have been more helpful.
I've never heard of an alternate kid's menu, that's not to say they don't have one.
I'd call WDW-DINE and ask for the dietary phone number to the Garden Grille and speak with them directly.