There is a parking lot tram from the DL parking garage to DTD. It lets you off right near the security entrance to the Esplanade, then you go through and either go left or right to one park or the other. The ride isn't too far. I'd say it is comparable to riding from the parking lots at WDW to the TTC. The garages are right next to the parks, but they bring you in in between to let you off.
Are you are staying at the Quality Inn on South Manchester Ave? If so, it is not very far from the parks at all, in fact it is within easy walking distance. You can cut through the parking lot of the Fairfield Inn (I believe it is) and McDonalds then you cross Harbor Blvd. and you're on property.
If it were me, I wouldn't even bother to drive and have to pay the $12/day fee to park in the garage unless it was an absolute MUST to drive, since the hotel is so close.