Hi Kate!
Strollers are an important part of your planning when traveling with younger children to Walt Disney World. Keeping the kids comfortable and happy means everyone stays happy!
Every park has stroller parking in set areas. That does not mean that every attraction has their own separate parking area. Usually you will find a central location that guests can park and then enjoy several of the nearby rides or shows. There are attendants in each of these areas but please know it is impossible for them to know which stroller belongs to which guest. Their primary job will be to have them parked in an efficient manner.
To keep track of your personal stroller it is recommended that you decorate it some way that personalizes it to you. You can add scarves or balloons or ribbons. Make sure it is nothing valuable as it will get used and worn as well as weather can take a toll on the decor. Also, never leave any of your valuables under or in the stroller during your time away. General things are fine but never leave purses, money, cameras etc.
All of the Disney parks also provide
Stroller Rental. You can rent single or double strollers and can rent daily or by a length of time visit. They cannot be taken back to resorts but it does help not to have to deal with them on buses and monorails and boats. It is certainly something to consider before your vacation.