Oh, to be 17 again.. I remember a trip around that age where I had different style and color sandals to go with each outfit for each park! I could totally handle the parks in flip flops, but now, not so much. I'm with your daughter - my go-to shoes for everyday stuff are boots, and then flats, and then Converse, but I know my feet will die in boots when I'm in WDW next week!
I have two suggestions; I usually wear Sperrys to the park. It's certainly a style choice, but they have great arch support, and you don't need socks. The beauty of them is they're boat shoes, so if they get wet, who cares! That's their purpose. I have a pair of gold Sperrys that I absolutely love and have worn so many times to DLR. I also have three pairs of Converse I rotate.
What I found to make the shoes MORE comfortable, rather than less is the following - if I'm wearing Sperrys or sandals, I use BodyGlide on my feet and I bring a stick with me. It keeps the friction at bay and I can slide the shoes on and off more easily. For my Converse, I wear low-cut, sweat-wicking socks. Target sells them. They're great because they pull the sweat away from your body, keeping your feet cool, and they offer arch support - they're basically running socks but they don't peek over the top of your shoes.
Finally, I invested in a pair of Sanuk flip flops. They're made from the same material as yoga mats. I was totally against the idea until I found a pair with a glittery leopard print in the strap, and I am obsessed with them. Totally wearing them to AK next week.
One other recommendation - I always rent a locker at DLR whenever I go, and I bring a change of clothes and a change of shoes, just in case, which I will probably also do at WDW next week. You could always bring a pair of flip flops or sandals as a back up, in case she hits a melting point!
Good luck!