Why don't you go to a nice resraurant in one of the parks (Epcot?) She can explore the park for a few hours by herself but you will be close. After dinner check-in with her, then if everything is ok, send her to explore more and you and DH explore. I would think in the parks would be the safest place. I don't feel safe at DTD by myself but I do it the parks. My local mall is a far worse place to be by myself than WDW but I still go shopping. At 14 my mom let me go places by myself and it made me more indepedent.
This is exactly what I would suggest. Maybe you could let the younger one stay with her sister, give them money to get a burger or something, let them have a cell phone, and just have them check in with you every 30 minutes.
Epcot would be my first choice, but the Brown Derby at MGM would be another.
At 14, my daughter spent 3 weeks touring Europe with a student group, so I'm a bit more relaxed than some. She has since been to India, Africa, and Europe (London and Rome, this time) with other college students.
I leave my son (14) alone all the time when we go out to dinner and he chooses not to join us, or isn't invited. He puts all the deadbolts on, and has a phone nearby.
He's bigger than I am now; he's more capable of protecting ME!