There are quite a few car rental offices in the hotels in DTD. If you are at SSR, you are very close. Just head over to DTD, then cross the street and you're there.
Budget also has an office at the Doubletree. Then you can return the car after you check in at the BW, and then take the DTD bus back to BW, or a lot of the rental companies have services that will return you to your resort.