With little ones, we have used our own stroller. At the end of the day, our children often feel asleep and having to carry them from the bus stop/monorail to the room could be so long! If your stroller is easily collapsable and easy to hold on to (in case you have to stand on the bus), it will make things easier.
Are you staying on Disney property? We have visited WDW during the Christmas week several times with toddlers and have found early entry one of the best things for us. We are morning people, so getting up early was no problem.
Early entry at the Magic Kingdom is absolutely worth its weight in gold. We go right to Fantasyland and park the stroller (easy to walk around with littles ones), ride Dumbo FIRST, and then walk on most of the other Fantasyland rides before the park opens.
We then do a couple of different things: We can get Buzz fast passes, then Tomorrowland Speedway (horrible lines if not done early), and then Toon Town when it opens.
On a different day, we go from Fantasyland to Frontierland and Adventureland as the park opens.
Early entry allows us to get so much accomplished in the MK with little waits. We then head out of the park around lunch (great time to wander through Main Street stores) to go back to the room for naps.
If you aren't at a Disney resort, go to a different park than the one with early entry. Also, keep checking the WDW website because the hours often change close to the holidays AND check the weather forecast. We have had several cold trips over Christmas (coats, hats, & mittens).
Character meals are also wonderful time-savers. The characters come to you! You don't have to stand in line to meet them. And, if you do go to an official character greeting, a cast member will take your picture with your camera.
I think if you keep things simple and don't try to do it all with toddlers the trip will be less stressful. Kids are easy to please - They will likely think the monorail is just as fun as other rides! The resorts (GF & WL) are worth visiting for a break to enjoy the decorations.
ENJOY yourselves! WDW at Christmas is so wonderful.
