Pandapants,
If you decide to rent at TTC, you can indicate you want to drop the car off at the airport. Since it's close by, there may be little to no extra charge for dropping at a location different from initial rental. It would certainly be less than the cost of paying for airport transfers on the return trip.
I'd advocate Beth R's suggestion to check into a week-long rental. If you add up what you will be spending on transportation from the airport to your hotel, for a two day car rental for visiting relatives, and returning from hotel to airport, you might find you fare better with a weekly rental car rate. You mention something about an airport hotel and a shuttle. If you have the rental car, you can still keep it until the day your flight actually leaves and not need the shuttle. And if your hotel is actually in the airport, then return the car when you check in there.
BTW, an advantage to renting at the airport is you have more than National to choose from. National is in the terminal. If you decide to rent for your entire stay from when you arrive, check into the rates for Dollar, L & M. I'm not sure if Avis and Budget are still in terminal, but that can be easily checked into.
Having Disney Club or AAA might help with rental discounts. Be sure to check National's specials online at their website. Much different pricing sometimes than through Travelocity, etc.
Hope this helps!
Sharon