Hello, Beth!
I'll bet you and your family are so excited about your upcoming Walt Disney World vacation! Your little ones are going to amazed at the magic, and you're going to love watching it all through their eyes!
Regarding strollers, we always preferred to have two strollers, so that if we needed to separate (i.e. one parent takes the younger one to the Baby Care Center for a diaper change while the other parents remains with the older child while she finishes eating, or goes on another ride) We found really convenient stroller clips, too, at Babies R Us, that clip the two strollers together (we used the more substantial yet lightweight umbrella-style, both with a flip-down top for shade). If yours come with a plastic cover, or if you find one at a baby-gear store, bring them. This will keep the little ones comfortable should you be caught in a rainstorm, and they will keep your strollers dry if you are in an attraction or restaurant while it rains.
If you change your mind once you're in WDW, though, you can
rent their very substantial double or single strollers for a reasonable price. There are also more substantial, but foldable strollers available for sale in select shops in the parks.
Have a wonderfully magical visit with your little ones in Walt Disney World! Be sure to send more questions as you think of them, too. We love to help!