National is on site and will come pick you up at your hotel and take you to their car center. They do NOT have EA service at the car center.
Alamo and Dollar are at hotels in the Downtown Disney (Alamo is at the Wyndam and Dollar is at the Courtyard). There are probably others that I don't know of there and you can walk to them from Downtown Disney.
I have used the National location on site and did not have any problems with it at all. I even got upgraded for free to a Premium car from mid-size. They came to DXL and picked us up. I am using them again in January.
They have a counter at the Car Center and the Dolphin. We have used them once without a problem and are using them again in July. Got a very good rate also!
Is National on site at the airport? Or is it at a satelite location? We have always used AVIS and have been pleased. In advance, THANKS for the feedback!!!