Ko Olina Area
Food stores in Kapolei include Costco, which should be useful for 13 people, with Safeway, Long's Drugs etc., and Walmart practically in a row a little further away from Ko Olina. The best restaurant in Kapolei is Thai Lao Rest., which is kid friendly because everybody behind the counter is Southeast Asian. However, 13 people would occupy about 1/3rd of all seats, so it might be best to go at off-peak hours. They open at 11AM. Burger King, etc. are available in the same area.
In Kapolei, in the strip mall makai of the theaters is a place called Brick Oven Pizza. I was impressed. Great Crust, very good range of toppings, nicely prepared, good service and the place was spotless. They also have a full bar. A long drive from town, but since you are out that way, I would definitely put it on the list.
There is also a Chun Wah Kam Noodle Factory in the same strip mall. Haven't been to that one, but in general they are pretty decent. Mostly asian noodles and sides.
I have also heard that the Aulani is expensive and the food not good. Next door is the Ihilani (a Marriott property) and they have a family style restaurant - Naupaka. Ihilani also has an Italian restaurant - Azul. The ravioli is very delicious. There is also a convenience type store nearby - I believe its the Island Country Market or something like that. Its an ABC Store with a deli in the back. There is also Koolina Hawaiian Barbeque which serves plate lunches. They might also be open for breakfast but I'm not sure. This is all in the Koolina resort. You can drive out to Kapolei where there are numerous chains to dine at (McDonalds, Costco, Wendys, etc.) and also a large Safeway. Hope you enjoy your stay - your kids will probably love the Aulani. Bring lots of sunscreen, they'll probably want to be at the pool all day every day!