Group and Family Friendly in Palo Alto or thereabouts
Lots of possibilities. Defining your price range and location would help.
Zibbibbo has a nice private area, as does Tamerine. Separate enough that whatever your toddlers do is your own problem.
There is no Korean within 5 miles that fits your bill.
For Chinese, consider Su Hong Palo Alto, in their new digs by the Los Altos border (easy parking). The university ave chinese joints are nothing to write home about. Or go further south to Trend, which might be less than it once was, but still a good time and I've seen toddlers there have a blast chasing each other around - even easier parking. Jade palace should also be considered. Melanie's written them up a few times. They're moderate on the informality scale, but large enough for your group, and with good ordering, very tasty. Although I'm a fan of crouching tiger, they're a little small for your group.
But you should consider indian. Passage to India fits your bill well enough, the food's good. I think they are doing buffet dinners these days, which might be overly casual, but check it out. I don't love the atmosphere at Suraj (very south edge of RC), but they have lots of space.
Coconuts I've been to twice and don't get where the "fun" comes from. It's a pretty spare white box of a room with some ethnic decorations.
1039 El Camino Real, Menlo Park, CA 94025
For my family fun is trying something new. I don't have a lot of chowhounders in my family so breaking out of the Chinese, Mexican, Italian, and burger rut to have Caribbean food is fun for them. Good service, live music, strong rum drinks, plates of fried bananas and spicy jerked chicken wings are a major change of pace for the "elders" in my family.
But its true, they do not have any rollercoasters or and its not Chinese food.