yes they most definitely will give you a kids meal! They basically let you order from the kids menu at Kona...we were offered 5 or 6 things and both my kids had different things, no problem at all.
Disney is most accomodating with any diets or requests, a couple years ago my son would ONLY eat grilled cheese sandwiches (thats right, No pizza, No chicken fingers, No hotdogs) We were at Mama Melroses and no grilled cheese on the menu but most restaurants would just make him one however they did not even have the bread to make it with! The chef himself ran across the park to 50's Prime time to get him a grilled cheese! We only inquired and had not pushed at all, we were expecting to just get him something later when the waitress came out with it!!! We were impressed to say the least!!!!!!!!