Hi Janee,
Thanks for your question! My advice would be to bring two light weight strollers, one for each of your children. Then your children will have access to them, not just in the theme parks, but also throughout the airport, the parking lots, and your resort. There's plenty of walking on a Walt Disney World vacation and I can guarantee you will use the strollers more than you think. As cute and cuddly as they are, tired children at the end of a busy day in the parks can be very heavy to carry. Strollers are a "must-have" for most children under four-years-old.
Overall, you'll also save yourself a considerable sum of money by bringing your own strollers from home. Currently
daily rental fees for strollers are $15/day for a single passenger stroller and $31/day for a double-passenger stroller. These prices drop a bit if you sign up for a multiple day rental plan ($13/day and $27/day for single- and double-strollers, respectively). However, keep in mind that if you rent strollers in the theme parks, you must turn them in at the gate as you leave the park. That leaves you and your husband to carry any sleeping children as you return to your resort. That makes a strong argument in favor of bringing your own stroller.
Whichever strollers you choose to use, be sure to tie something distinctive to your strollers (a colorful bandanna, for instance) so that they are easy to spot upon exiting rides. You're going to see plenty of strollers in the theme parks and it helps if yours are easy to identify.
Your children are really at a magical age. Soak up every precious moment with them at Walt Disney World!
Best wishes,
Jill