Shuttles over there typically are limited and not free. I would check your resort to find out exactly what they offer. I would also check closer to your trip as the policies and schedules might change.
You may find the hours don't fit your schedule or they cost the same or similar to ride-sharing, but lock you in to certain times. You are paying $300 a day for park tickets or more and don't want to miss time because of a bad shuttle schedule.
With a 2-year-old I would rent a car. I would be hauling a stroller and snacks and would want the storage and freedom to go whenever and where ever I want. You never know when you might have to bail with a young one.
There are a lot of ways to save money on a Disney trip, but my 2 cents making sure that the transportation works when you need it is worth paying for.