Welcome to planDisney, Pamela!
Strollers are vital if you're taking little ones to Walt Disney World. I've just returned from a trip myself and I'm still recovering from walking 10+ miles a day pushing a double stroller!
Pamela, the current rules state that strollers larger than 31” (79 cm) in width and 52” (132cm) in length are not permitted. Also,
stroller wagons are not permitted. Therefore, according to the current policy, the Evenflo Pivot Xplore All-Terrain Stroller Wagon would not be allowed in the theme parks. I realize that's not the answer you wanted to hear, Pamela. However, let me mention a couple of other options.
Renting a stroller at the Walt Disney World Resort is very simple. You can rent them near the front of all four theme parks once the park opens. You can also rent them at Disney Springs. At this time, you can't reserve a stroller in advance. However, even though availability is limited, there are ample strollers to go around. Therefore, I doubt you'll have any trouble.
You can even purchase a Length of Stay Rental for the number of days that you plan on being in the theme parks. This will actually save you money over the daily rate. You'll just need to show your receipt on any subsequent days. You can't take your stroller outside of the theme parks. So you'll have to pick up a new one each day. One of the cool things about renting a stroller is that they have a snazzy Mickey and Minnie design!
Another option for you is to rent a stroller from an outside company. There are several companies that deliver strollers right to your Disney Resorts Collection hotel. For example, ScooterBug is an official Disney Featured Provider and will drop off and pick up strollers at your hotel. You don't even need to be present! You can even pre-order a stroller ahead of time. My family have used this company in the past and had a great experience.
I hope that's helpful, Pamela. I hope you have a wonderful time at The Most Magical Place on Earth.
Mike