Hi, Kelly!
The only time you would need to fold up your stroller is when boarding
Disney buses. Since you plan to drive to the theme parks, you will not have to worry about it. Once you are in the theme parks, there would be no reason to fold your stroller (except if you wan to take it on the Walt Disney World Railroad, where it will need to be folded to fit). There are actual stroller parking areas for you to leave your buggy when you are heading on attractions or going to eat.
If taking the
monorail, you will not need to fold your stroller, you can roll it right on with the kids loaded in! This is very convenient. When taking boat transportation, some boats you can keep the stroller upright, while other smaller transport boats will require you to fold them up. Ask your boat captain before boarding.
I hope you find an easy system to maneuver your stroller in Walt Disney World. If you decide to simply leave your stroller at home, you can always
rent one at any of the theme parks or Disney Springs. Either way works, so figure out what will be the best for your little Mouseketeers!
Cathy