Hey there, Shauna!
We're so happy that we can help you plan your upcoming Disney vacation.
The strollers that are available to rent at each park cannot lay back and are made of a firm plastic material. However, they do have a pretty large back pocket for you to hold your items and a shade/cover. A medium size diaper will fit in it perfectly.
Whenever we visit the parks, we rent a stroller from an area Orlando company that delivers to our hotel or resort. They recline flat, which is perfect for a sleeping baby or child. They also have a medium size storage area underneath the seat. I've gotten a large bag underneath and plenty of souvenirs.
To rent from one of the area Orlando stroller companies, you will need to visit their website and pay for the rental in advance. The
stroller rental at the Walt Disney World theme parks is available on a first come, first serve basis and you'll pay for this stroller at the rental location.
Shauna, I hope this helps you. Have the most magical time ever! If you have more questions, don't hesitate to visit with us again.
Korliss