Hi Amanda,
Thanks for visiting the Disney Parks Moms Panel. We're happy to help with all your planning questions.
Walt Disney World is a comfortable destination for guests of all ages, including little ones. You will find stroller parking areas outside all attractions and most table service restaurants. Locking is not necessary or even permitted for safety reasons. I don't recommend that you leave valuables such as cameras or phones in your stroller when it is unattended. But in many years of using a stroller at Walt Disney World we never had an issue with anyone tampering with it or our things.
I always packed an extra rain poncho for the stroller, in case our stroller was parked outside when a storm threatened. (I never bought the special stroller covers you can buy at the baby store; I simply got an extra disposable one from a discount store to throw over the stroller.)
Because your children are small, you will be excited to hear that there's a comfy
Baby Care Center in each of the four theme parks, a place to nurse, relax, eat or change diapers. I've attached an informational video about the centers to this answer for you.
You also may want to review the information about
visiting Walt Disney World with preschoolers found here as you make your plans.
You will find milk available for purchase at restaurants and in the gift shops/food courts at all Walt Disney World resorts. And you are welcome to bring drinks and snacks for your children into the parks with you.
Please let us know if we can offer any other advice to you as your vacation nears, Amanda. Enjoy your visit with your family!
Wilma