I think Kona Cafe is a lovely place to enjoy a quiet, relaxing meal with some wonderful choices from the menu (it is famous for its decadent Tonga Toast at breakfast!), but with young children, I'm partial to 'Ohana. At breakfast, your family will be able to enjoy dining with Lilo, Stitch, Mickey, and Pluto. The meals are served family style, so you don't even need to spend the time making choices. You are just brought lots of yummy offerings! At dinner, a large fire pit will work its magic cooking up an amazing assortment of all you can eat shrimp, sirloin, turkey, and pork loin as well as starters, sides, and desserts (vegetarian and alternative children choices are available upon request). But what makes it fun are all the games that are played throughout the evening like coconut pushing races and hula hoops contests. Some of the tables even have views of the castle, so you can watch the fireworks if you are eating at the same time!
Remember that 'Ohana means family, and you'll have a great time with yours while there!