Hi Douglas!
I also have 2 children ages 2 and 6, so I'm certain we'd have similar "war" stories to share :-)
I'd definitely go straight to the park and let the kids get some of that energy out. Plus, if you go somewhere and rest first, all you'll hear from the kids are "Can we Can we Can we GO???"-smile
Anytime we visit with the children, and we arrive before check in, we get our tickets (Keys to the World card) from the front desk and head straight to the parks. You'll see a burst of energy from the kids early on, then sometime between 12-2pm, they'll be looking for somewhere to lie their head for a nap.
In addition, getting to the parks when they first open is generally a little less hectic than getting there at, say, around 2pm.
Good Luck on your first trip! Hope you and your family have a magical time!