Hi Tamra,
The double strollers available for rent in the parks are the "side-by-side" style. They are actually comprised on one "long" bench for two children. They are similar to a jogging stroller, except that the seat is a hard plastic (think, lots of kids, easy to clean!) They all have a large canopy, and a pocket area for some small belongings. They are very easy to maneuver and push. I'm a stroller collector and find Disney's to be a pleasure to use. Kids seem to like sitting in them, as they are low to the ground and afford a great view of what's going on.
There are pros and cons to renting versus bringing your own stroller. While strollers are available in each of the theme parks, water parks and at Downtown Disney, they are not available at the resorts, the Boardwalk or other areas outside of those I mentioned. If you think you'll need a stroller at any of these areas, consider bringing one. In addition, Disney tends produce very sleepy kids! My kids have knack for falling asleep just as we are exiting the park. The thought of carrying sleeping kids out the exit and over to a bus or monorail line scares me, so we tend to bring our own.
If your kids use their stroller infrequently, and you don't think you'll need it to maneuver through a busy airport, around your resort, walking to and from the resort/park buses, etc. renting might be a great option. Click
HERE for current pricing and rental location information. You can either rent by the day or purchase a "length of stay" rental for your trip.
Have fun!