Hey Lea,
Glad you love the panel - we're loving you right back as it is an honor and privilege to assist guests planning a trip to the most magical place on earth.
Strollers are available for rent at each of the four theme parks and Downtown Disney. Rentals are on a first come basis and no advanced reservations are taken so you can only do it once you enter a park. Single strollers are $15 per day & doubles are $31 per day (always subject to change). If you plan to rent for multiple days, consider a Length of Stay Rental which will save you a little money ($13 per day for singles & $27 per day for doubles). Keep in mind that you aren't guaranteed a stroller will be available even if you purchase the Length of Stay Rental.
Strollers must remain in the park from which they were rented so if you park hop during a day, you will be required to turn in your stroller before you leave the first park and then show your receipt at the next park to get another stroller - subject to availability at that park.
There are venders in the Orlando area that rent strollers. One of the best I've found is
www.orlandostrollerrentals.com. The offer free delivery and pick up to resorts in the Orlando area. They have several stroller types to choose from. They will have your stroller waiting at Bell Services when you arrive and will pick it up there after you depart.
Bringing your own stroller or renting from a local vendor allows you to use the stroller to get to and from the parks, your hotel and throughout the WDW resort. Please feel free to come back with more questions.
Wishing you many magical memories during your trip :-)