Hi Melodie:
Strollers are available for rent , subject to availability, at a variety of locations throughout Disney Theme Parks, Water Parks, and Downtown Disney. Disney strollers are not available to rent at Resorts. I highly recommend bringing your own stroller or using a stroller rental service to use outside of the Parks. My family uses a local Orlando stroller-rental service, orlandostrollerrentals.com. They are familiar working with Disney World and conveniently deliver and pick up the stroller right from your Resort. If you bring your own stroller, make sure it easily folds up if you plan to use Disney's bus transportation.
I highly recommend making advance dining reservations for most or all of your planned sit-down table service meals. You don't need reservations for quick-service meals.
Dining reservations can be made up to 180 days in advance, so the earlier you plan, the more choices you will have as some restaurants tend to book up early. If you do not have advance dining reservations, you can still try walk-ups. However, at popular restaurants, you may be asked to wait a while or turned away. With young children who may not be comfortable waiting, you are probably better off making advance reservations.
Some great fun family restaurants include: Chef Mickeys (dine with Mickey and his friends); Biergarten (all-you-can consume German-style buffet); 50's Prime Time Café, (American comfort food and fun service); Whispering Canyon Café, (Old West themed family-style restaurant); Raglan Road (modern twist on traditional Irish pub food); T-REX Café (dinosaur-themed family restaurant); 'Ohana (for dinner), (Polynesian family-style restaurant); Coral Reef, (wonderful experience where you can dine in front of stunning underwater views).
Enjoy your vacation.