If you are staying at the Polynesian, I wouldn't go to Chef Mickey's. To much travelling. Getting to the park is hectic enough. The food at Ohanna's is very good. If your kids are really into the Characters, Chef Mickey's is probably a little better. Many more choices at CM's buffet also. Ohanna's is a sit down, all you can eat.
My suggestion is to do what a previous respondent said. Go to Chrystal Palase instead. We normally make the latest possible breakfast reservation and treat the meal more as a brunch. On the day of early admission to the park, we eat an early snack at the hotel to tide us until our reservation at 10:45 am. We hit the park and do all of Fantasy Land, Space Mountain, Motor Speed way, and get a fast pass for Splash Mountain. Then we go eat our brunch, save money by skipping lunch, finish the park and head back to the hotel in the early afternoon to beat the heat and crowds.