Welcome to the Disney Parks Moms Panel Anna ~
I love to see that you are planning ahead! If you are traveling with a 2 year old and a newborn, I would bring my own stroller. I personally don't think the strollers available for rent in the parks are very good for children that may want to take naps during the day. The strollers are made of hard plastic and do not recline so napping would be difficult. They do have a canopy and have a little (not a lot) of storage space. I would not put a newborn in the rental strollers in the park and would not try to put a car seat in either.
The picture that is shown on the
stroller rental link on the Disney website is not a picture of the strollers for rent in the parks. You can see a picture of the single strollers and double strollers on the website AllEars.net. If you search for "strollers" on their homepage, the first link shows a picture of both.
If you are flying, bringing your stroller from home may assist you in getting through the airports. Another option is renting from a private company in Orlando. There are some local companies listed at the bottom of the Stroller Rental link on the Disney Website. They will deliver to your resort so your stroller is there when you arrive and pick it up at the end of your trip. A local rental company may even save you money versus renting in the parks.
I answered a question for another Guest with some
tips on strollers that you may also found find helpful.
Please feel free to visit us again with all of your questions. We're hEAR for you!
Wishing you minnie magical memories :-) Allison V.