Hi Lauren,
I am glad that you are planning ahead to keep your infants cool and happy during your trip. The average high temperature in Orlando in May is 88 degrees Fahrenheit, so it may be quite warm, but not as hot as it will get later in the summer. With a little advance planning, you can have cool, happy babies at Walt Disney World.
First, I do like your plan to visit Epcot. It is generally the theme park that I like to visit the most when it is raining, because you can do so many things once you are inside one building. The same would hold true for getting out of the heat. I bet your little ones would love to see
Journey into Imagination with Figment. This colorful ride was my daughter's first attraction ever, and she experienced it when she was only 7 months old. I also suggest that you take them on
The Seas with Nemo & Friends, on which they can ride through the story of Nemo, ending in an amazing aquarium full of sea life.
At Epcot, and at all of the Disney theme parks, I suggest that you take advantage of the
Baby Care Centers. These offer a quiet spot to feed and change your infants, or just to quietly relax in air conditioning away from the hustle and bustle of the theme parks. If you can arrive at the theme park early, even a little before the scheduled opening of the theme park, you will be able to experience many attractions with shorter lines in the coolest part of the day. Also, if your little ones take naps, heading back to your resort for naps should help to keep them cooler and happier.
I am limited in the amount of space that I have to answer, Lauren. Please do not hesitate to ask if you have any further questions.