Hi Melissa!
Welcome to the Disney Parks Moms Panel! My son turns three in a few weeks and I spent so much of 2015 researching strollers to find the perfect one that would work for our family. (But mostly my Disney Parks obsession.) There are SO many new types and styles that have hit the parenting market since then, but there are two
stroller requirements at Walt Disney World Resort that remain the same: the maximum size, and the wagon rule.
The size limit of strollers is asked to not exceed 36" x 52" as this is the width of most doorways and aisles. I'm happy to say that double strollers can be side-by-side or in-line, with the seats facing any which way. I have a Vista, and while I've encountered some tight spaces in just a few shops, I still love my decision.
The wagon stipulation means that traditional or new-fangled wagons that are pulled are not allowed, for a few good reasons. Wagons or other pulled strollers usually have less control than those that are pushed. There are also many spots across Walt Disney World that have traditional sidewalks and curbs. I'm a terrible wagon-puller, curbs get me every time. (I've accidentally dumped the contents of a wagon on multiple occasions on the same spot of the sidewalk in front of my house.) So I'm glad that Disney has thought ahead to save me from myself.
Pro Tip: Check the weather before your arrival and bring a stroller cover from home. Ponchos work great in a pinch, which can be found at almost every souvenir kiosk or stall.
Bonus Tips: Standing boards that attach to the back part of a stroller so an
older child may stand between the stroller and the pusher are allowed.
I hope this helped, Melissa, and We'll See You Soon!
~Kristen