I would recommend a regular stroller with a sun shade. The heat and sun can be brutal in Florida. (With something like above, it definitely could not go on Disney buses, and possibly the skyliner - all strollers must be folded on buses). My suggestion, leave it at home!!
According to Step 2, its a ride toy. It is suggested for ages 1.5-3 years. Extending that to even four or five. It definitely cannot be reclined for any "napping". (The average guest walks 8-12 miles per day). Anything you bring into the park, is at the "discretion" of security. I'm not sure, it will get through. Its hard plastic, sits close to the ground (causing a tripping hazard). Guests have been known to run into strollers, etc.