We took our 4 yr old to Tiffins twice on our last trip. No view of animals, but there is animal decor. He didn't really care about the theme of the restaurant, but that would have been true almost anywhere except maybe Coral Reef. He ate the food both times, was pretty well behaved, and we had a lovely meal. There were other young children there both times we were there, although the vibe is definitely quieter and mature. I think at 11 and 13, your kids will probably be much calmer at any dining table than my 4 yr old, lol.
I see others mentioned Sanaa. We ate there for the first time this last trip and we loved it! All the AK Resort sit-downs are good options, in our opinion.