At DHS there is a little bar over by the Studio Catering Company (the CS that's right next to the Honey I Shrunk The Kids playground) called High Octane Refreshments that serves really decent drinks. They have a pina colada that comes out of a machine, but it's really good. Actual bartenders to mix drinks, too. And yes, you can carry an adult beverage out of the Tune In Lounge, tell them you want it to go and they will put it in plastic for you.
At AK you can also either drop into the bar at Yak & Yeti or pick up a frozen boozy beverage at a window near the CS.