You might ask your doctor before you go if he/she can recommend anything. Like the previous posters mentioned, taking ibuprofen will help because of its anti-inflammatory properties and low potassium is really linked to cramps. If you go during hot months or are prone to sweating, you can be sweating out that potassium faster than you are replacing it. Bananas are great for this -- lots of athletes do this, but your doctor may even recommend supplements.
The other thing that really helps is -- bring a spare pare of shoes and socks (that are already broken in). Change halfway through the day. Maybe you need something with a higher arch than Teva's all day? Swap out with something else halfway? I prefer Saucony and Skechers. Even if they are the same kind of shoes, they will be slightly worn in different places. Keeps pressure points in different areas. Made all the difference for me and my DH. We also keep face wipes to use to wipe down feet and calves when we change. Refreshing.
When you do stop during the day for food or just to rest, prop your feet up on another chair. You would be suprised how quickly that helps. Plan for sit down rides like Ellen's Universe of Energy, the Great Movie Ride, Tommorowland Transit Authority, etc. Spread them out so you don't exhaust yourself too early in the heat of the day.
The hot tub sounds heavenly! We always shower morning and night at Disney. Really relaxes you after tromping ALL over WorldShowcase. Don't do Epcot on a day you are already tired. If your trip allows, take a day or a half day off from the parks to hang out and swim. Try Epcot the next day. We forget how big it is until my DH sends me back and forth between Voices of Liberty and OffKilter performances all day!
Have fun!