I think there may be several things contributing to the problem here. First, does she use cups with lids at home? If not, she probably wants her McDonald's cups and Sonic cups to be JUST like the ones at hoe, i.e. lidless. Second, I think she's probably a little young to be using regular cups away from home. While things have a regular routine at home, there are so many distractions at other places. It's almost impossible for a child that young to focus on keeping a cup upright when there are so many shiny, colorful, noisy things and poeple to watch. Especially if your daughter is a hands-on learner and wants to be part of everything she sees.
I'm sure there are a lot of solutions to your problem, but here are a few things I thought of.
1. Let her drink from lidded cups with straws at home. You can find them in the baby or kid section with the sippy cups at most stores like Walmart, Target, or Kmart. If she gets used to keeping the lid on at home, she'll be more likely to keep it on away from home.
2. Let her use sippy cups away from home and regular cups at home.
3. Find a plastic lidded straw cup with a screw on top that she can't remove by herself, and make it her special outing cup.
I'm sure you'll find a solution!
T.