If I were you I'd keep it simple when going into the parks. In other words, just take the D7000 attached to the 16-85 VR only into the park. As a resident of West Palm Beach, Disney World is in my back yard (so to speak). With 9 year old twin kids I've gone there several times in the past years - all visits were before getting my Nikon D7000 though. Much of my reasoning depends on who's going with you...spouse/friend, in-laws, kids, how many and how young?
There's so much to see no matter which park you go to and there's lots of color. You'll want to capture the color on so many of your photos so taking the 70-300mm zoom will cause your pics to miss a lot of whats right around you. In addition, Disney is just not a place that would cause you to need the 70-300 lens. Everything you'd want to get a picture of can be taken with that 16-85. If you go to Animal Kingdom...my suggestion...enjoy the sights....shoot what you can with the 16-85 and don't hassle with lens changes just to get a shot of the animals. That 16-85 is quite capable of capturing everything you'll want to.
You can still bring the 70-300 and SB-600 on vacation for whatever you might want them for but no need to bring them to the parks IMO. As far as the Sigma 10-20, personally, I'd leave it at home unless you think you'd like to get some super wide shots from within the park. I think 16mm is wide enough and taking time to change lenses would take you out of the moment of just having fun.
If you visit one of the in park restaurants and there are characters around, once again the 16-85mm + on camera flash is all you'd need. Night-time, just up the ISO and shoot away. If you're going to the Magic Kingdom try to stay till dark and get a few pics of the castle at night. It's beautiful. VR will help a lot there. Also be sure to catch the character parade down Main Street. Happens twice per day I think. It's quite the photo op.
About the camera bag. I looked at it on-line. It looks good if you're only bringing the camera/16-85. Getting on some of those rides will require you to sit with that bag between your legs but there's usually ample room for that. Just hold on tight. Wouldn't want your new camera flying out of the Dumbo ride : )
I'm suggesting taking only one lens to the park also because as the day goes on, you'll appreciate a lighter kit.
Most importantly...have fun!