Hi, Anne!
Welcome to Disney Parks Moms Panel!
We have traveled to Walt Disney World with many 3-year-olds as well as with folks with mobility issues, so I completely understand your concern for their comfort.
First, bring your own stroller for your daughter. This will enable her to cover the distance of some pretty big parks without her little legs giving out, causing you to have to carry her. Should you wish to rent a stroller inside any
Walt Disney World park, take a look at this helpful link regarding
stroller rentals. Truly, the distance adults can walk around every park can be far too taxing for a little one, so consider the use of a stroller to help her go the distance (Oh, and that stroller can carry your heavy bags, too! Win-win!)
Regarding your mother, post-knee surgery, I would suggest that you map out your touring based on distance from park entrance and transportation. Should your mom need to rent a wheelchair for this distance that her knee may not be ready to handle just yet, you may rent these at Walt Disney World, too. This great link on
wheelchair rentals will provide you with information on wheelchair rentals as well as
Electric Conveyance Vehicles.
However, should your mom just need to walk a little more slowly, without additional assistance, I suggest that you opt for attractions that allow her to sit between bits of walking. Look at each park map, judge the distance she'll walk, and be sure to plan your dining locations within a comfortable area for her, too.
We can easily provide you with more detailed touring suggestions, Anne; be sure to ask!
Andrea H