Potluck

Thank you so much everyone!

For vegetarian and kid friendly, I'd probably consider a mac n cheese. While I might serve one in my house with cauliflower or butternut squash mixed in, sometimes a group of four year olds won't touch it if it has veggies in it. For something like this, it depends on your crowd. As long as there are lots of vegetable side dishes and salads available, I might leave the veg out of the casserole.

If you know you have adventurous kid eaters in your group, maybe a vegetable lasagne?

You could coordinate with other parents bringing mains so that someone brings a vegetarian dish.

The all time most popular dish for kids and adults that I've made is this:
http://ruhlman.com/2010/05/macaroni-and-beef-with-cheese-%E2%80%94-childhood-love/

Do not, I repeat, do not, leave out the fish sauce! I have made dishes like this a million times but that touch of fish sauce really adds something.

you can make some macaroni cupcakes with lots of veggies in it. they look pleasing to kids and healthy and kid;s favorite thing pasta or macaroni

Seriously, if the kids are happy, the parents are happy. So think about what makes your children happy and multiply up.

Spring roll (the rice paper kind) wrappers with veggies would be good. (the dipping sauces for that might be messy tho)
Is their coordination between the parents? So no overlap?
Homemade chicken or turkey nuggets would be kid friendly.
Mini Pizzas...just roll out your favorite pizza dough and use a biscuit cutter to make little pizza bites---you could do veggie option for those too.

Oh, I am so with AntoniaJames. Pasta, lots of cheese, meat or not so as to please vegetarians, and you'll be the belle of the so to speak ball.

Kids really like baked ziti and similar baked pasta dishes. You could do one with meat (use Italian sausage and a really nice pecorino) and one without. Easy to make ahead, easy to transport and not too messy to eat. Sounds like fun!! ;o)

If you're up for it, be the person who brings a vegetarian main as these are often forgotten. Quiches are excellent since they're often delicious when not freshly warmed. Hearty bean soups made in your slow cooker are also great because, if you have a cooker that's easy to carry, you can bring it & warm it in the vessel in which you cooked it!