No, I don't give my kids the car keys and let them go off on their own, at ages 16 and 13. Especially to our local movie theater, where the wanna-be gang kids hang out, where I've called 911 because they were beginning to 'rumble' in front of dd13's dance studio, which is at the same stripmall as the movie theater.
Yes, I've dropped the older one off at
Walmart with friends, but I did not like that situation at all - of course she needs to learn how to handle being an adult and she needs experience with the 'real world', so I let her, but I don't have to feel comfortable with it. Of course I will let her become a responsible, capable adult, but there are too many good kids dying, getting hurt, just being in the wrong place at the wrong time, for me to not feel uneasy about her being in certain situations.
To the OP -ask your kids what they would do if something happened to one of them at the park - if one got separated from the others, if one got hurt, if someone got rowdy in a line and punched one of your kids in the face... After the 'teacup incident', I'm not going to be surprised by anything happening at WDW!