It depends what your kids like to do, and what you want to encourage them to do. There are lots of shorter hikes/walks around various geyser basins, to see mud pots and waterfalls, nature trails of various sorts, etc. How many days are you planning for Yellowstone? 2 full days there, you'll be skipping a lot of stuff, which is ok if that's what you can do, but not preferable if you can swing more time. One thing I might suggest is have the kids look for wildlife while you are driving around the park (and there is a lot of driving) - make it a contest if that will help. If the kids aren't that much into it, spend the daylight hours "doing" the park and come back to the CG for some pool time (enclosed pool at the KOA there) and supper.
As for meals in the park, picnics can be fun, and picnic grounds are abundant. There are also plenty of casual places to eat in the park - the Yellowstone General Stores have ice cream & burgers, there are delis in some of the hotels & lodges, etc.
Activities in the park can be pricey, but horseback riding is available, boat rentals &fishing expeditions at Lake, etc. - all at a cost. One activity that isn't cheap but which the whole family may enjoy is the cookout/stagecoach or horseback ride at Roosevelt Lodge. Reservations well in advance are a must. All of these things can be booked through Xanterra - check their website.