I recently moved to Orlando from the Washington DC area. DW and I have driven back a few times, taking anywhere from 15 to 16 hours each way.
We drive through the night, taking turns driving and sleeping, switching about every 1-2 hours whenever the driver gets even a little bit tired. I would only recommend this with someone you trust to wake you and switch drivers before they get sleepy. The advantage is that the trip only seems half as long (since you are sleeping the other half). Also, we avoid the traffic and congestion.
We also drove this summer to Cape May, NJ by way of the Chesapeake bridge/tunnel and up the Eastern Shore to the ferry. It took a few extra hours.
I just flew to/from BWI with some relatives on Southwest. All of the seating is unassigned. Since they had a child under 4 years old, the entire family (including me) was allowed to pre-board the plane, so we got our choice of seats before anyone else. I really would fly if possible; it does save a lot of time.
I'm not sure if you knew this but at checkout, you can leave your luggage with the bellhops at the hotel. They will give you a receipt. You can then spend the rest of the day in the parks, and come back for your luggage afterwards. There is no charge for this, but tipping is expected.
Hope this helps. Good luck!