Hi, Thaer!
I think you might find that the
rental strollers at Walt Disney World might work out for you. I was just looking back through some pictures, and I was able to use a double stroller when my kids were 6 and 3. Based on my pictures, it looks like they fit just fine. Now chances are they were complaining because they were probably annoying each other, but that's the life of 2 little Mouseketeers!
The rental strollers are actually just one big seat and their little legs can stretch out. They are made of heavy duty plastic, so durable for your 2 kids. My kids loved them, and I found them to be very easy to push and maneuver. You can rent these daily or save a few dollars and pay ahead for multi-day. Strollers remain in the parks and cannot be taken back to your resort.
I hope the rental strollers work out for you! I found them to be a lifesaver when my kids were younger. Their little legs will get tired after a day of walking, so I think your plan to rent a stroller is a great idea. Have fun!