You could also get a taxi to ferry you between the various resorts, I suppose. A rental would probably be less than that for the day if you used taxis for every jump. Which hotel are you staying at? There are several places to rent a car on or near Disney property.
I think it would be possible to streamline the travel via Disney transport such that it wouldn't be TOO bad.
Take the boat from SSR to OKW
Take the bus from OKW to MK and hop the ferry over to VWL.
Take the bus from VWL to MGM and walk or boat over to BCV and BWV.
Then if you want to go to AKL as well, either take the bus to AK and transfer busses or take a cab directly.
From your last stop of the day, you can bus back to DTD and enjoy a leisurely stroll home.
It certainly wouldn't be my first choice, transport-wise especially with a preschooler along, but it wouldn't necessarily be all that traumatic, given that you could have as many as three scenic boat rides and nothing pressing scheduled for the day, unless you have a couple of meal reservations. The hardest part would probably be the waiting for the bus or boat to arrive.