When you stop at the guard kiosk at the entrance to resort, they'll give you a 3 hour parking permit and direct you to the public parking for visiting the resort/restaurants/shops. They restrict those spaces to 3 hours, and have been known to tow cars with no permit or over time limit - they do this so people don't use the resorts for "free" parking instead of paying at park lots...and also to make sure hotel guests staying at that resort have spaces for their own cars.
But just ask them where to go for valet parking...because IF you pay to valet park at that resort (Yacht Club/Beach Club) you CAN leave your car there while you go to Epcot - the only time limit on valet parking is if you leave the car overnight, they'll charge you another $12.) Valet spaces are not limited -- they will just park your car elsewhere if need be...and they go fetch it so no big deal for you. Even though we'd have free parking in the Epcot lot (staying at Disney Resort AND we have AP), we still valet park at the Epcot resorts often...will cost you $12 to valet park (plus $2 or $3 tip when you pick up your car.) It's a great way to eat at Epcot resorts, and then enjoy the park. And the best part is, at the end of the night, you just exit through the International Gateway (between England & France), go to the valet desk, and they go get your car. No waiting for a tram, no hike across a parking lot & no long traffic snarl getting out of the park's lot. They pull up with your car, and away you go--no lines. It's well worth the $14 it'll cost you.
