As far as stuff to do that's family-friendly, off the top of my head I can think of this place called Hey Day just south of OKC near Norman? You might look it up online to see if kids that age would like it (because I know nothing about the interests of young children), but they have arcade games, laser tag, mini golf - stuff like that. Also, while it's most likely going to be really hot, there are a few parks around - Lake Hefner usually has a bunch of people riding bikes or skating, and they have a park, and there are a few other parks.
Restaurant-wise... Good local pizza can be found at Hideaway Pizza (thin crust Margherita pizza makes me drool) and Ted's is a popular Mexican place that has no problem making substitutions to make something veg. Like Brandon said, other than a few Indian places that have lots of veg options, I haven't come across any true vegetarian restaurants in OKC. Norman has a veg deli if you end up down there, it's called The Earth and their food is yummy. Does that help??