This really is a personal decision and depends greatly on the double stroller you have available to you. When we were in your position, we opted for 2 lightweight singles. Partly because my 3 yr old was very tall and not that comfy in our double at the time and partly because our double was too hard to push when it was fully loaded with 2 kids, diaper bag, camera bag, etc.
How I finally made my decision was by doing a "trial" run. I packed up the diaper bag, camera bag, changes of clothes, ponchos, stroller rain covers, snacks, drinks, etc, and put it all, along with my kids in my double stroller and went for a 2 mile walk with them. By the time I was done, I was exhausted and my arms were killing me, lol! I knew right then that I wouldn't want to push that around disney for a week in the heat of the summer. Perhaps if I had a different double my decision may have been different but it just didn't work for me with ours (it was a graco front/back).
So, you might want to do a trial run and see how you feel about it afterwards. If you can handle a nice long walk fully loaded, you might want to bring your double. If not, opt for two singles.