Do you really need a stroller at Disney?
Yes. I'm not ashamed, I will insist that my kids use a stroller at Disney until they physically don't fit in the stroller. This means we can pack a little lunch box with an ice pack for fruit, snacks, and cold drinks and not have to carry that weight all day. That luxury will be ending very soon for us, but I can't emphasize this enough: even if your kids haven't been in a stroller at home for years, they will use it at Disney. A stroller can prevent meltdowns from tired kids, you can move through the parks more quickly, and from a safety standpoint, you won't fear losing your kids in the most crowded areas of the park! Additionally, you will love being able to put stuff in the stroller all day instead of becoming the inevitable sherpa for your kids snacks, souvenirs, etc.
Options: We borrowed one from a friend, and if you have a good jogger type that folds up you can bring it along (my fav is the CityMini Double, but now have to go with a single, sadly). But if you don't own a stroller anymore, or don't want to deal with it in the airport, you can rent one from Kingdom Strollers for about $65 for the week, which includes the rain cover and cooler. They deliver the stroller to your hotel and pick it up from the bell stand after you check out.
Alternatively, you can rent a stroller in the parks each day, but it's pricey and you cannot leave the park with the stroller. This means potentially carrying sleeping kids all the way home! So just think about how you will be using the stroller - if you are staying on the monorail you can let kids sleep in the stroller all the way back to the hotel room! If you stay in the Epcot area resorts many of them are walkable from Epcot and Hollywood Studios.
Sleeping Beauty agrees: Using a stroller makes any Disney trip more fun for kids and parents alike!