None of the offical Disney hotel honor starwood cards. However since you hare a member of
AAA and starwood you can apply for the AAA starwood members card that allow you a 4:00 pm checkout (when available and a room upgrade if available.
Now the Swan and Dolphin resorts are Starwood properties but they are not owned by Disney however they are on Disney property. They are located between the Yatch/Beach Club and MGM Studios.