That's why Dragon Dance sets exist. VGCs are... what? 2 on 2 this year?
Politoed should have ice beam (quiet so his weather sticks in weather-battles?), Kingdra should be swiftswim w/ both ice beam and dragon meteor, and Weavile should have maxed out speed w/ ice punch of something - right? I really don't see why you should have a dragon problem. In fact, with so much dragon-hate, I could see leaving Dragonite on the bench - if I recall correctly, 2 on 2 requires you to take 4 pokemon, not 6, into battle.
Depends on your team. I like running Leftovers on the hope that you can recover your mock-focus-sash. However I think the idea behind the berry is that it lets you survive an dragon meteor/outrage that would otherwise kill you at full health. VGCs should have a lot of Garchomp, I suspect.
I'd have to know your full team to know for sure. The less fake-out/followme/whatever users you have, the more you need to protect Dragonite w/ his item.