You can go online and check out
Alamo/National and see what kind of deal you can get renting at the Dolphin. You can also rent from A/N at the Car Care Center, over by the entrance to MK....you can call them beforehand and they will come and pick you up. The Dolphin does not offer that, but it's pretty easy to just walk over there from Epcot..that's what we do.
If you decide to rent through another company, you can check out the online sites and see which ones are located in the hotels in DTD. I know that
Budget is located in the Doubletree....you can make arrangements for them to pick you up and take you to their office, or just go to DTD and then walk over to the Doubletree Guest Suites.
When it comes to moving from one resort to another....you have a couple of options.
1. Disney will move your bags for you. Hand them over to Luggage Assistence first thing in the morning. Tipping is expected. Then, you can expect your bags to get to AKL later in the afternoon...I have yet to get my bags before 5pm. And again, when the bags are delivered to your room, tipping is expected.
Then, head off to a park for a few hours and at lunchtime, head over to AKL from that park, and get checked in.
2. If you have your rental car at this point, you can just load up the car with your luggage and drive over to the AKL. If you luck out and are able to get into your room, terrific. Take your bags right to your room. But, if the room isn't ready yet, just leave the bags in the car and then head back later in the day to get settled in.
3. If you have no rental car, you can take a cab. Between those two resorts the fare should be pretty small. Take your bags with you. If your room isn't ready yet, leave them with Bell Services...tipping is again expected. Return later in the day, when the room is ready, and call to get your bags brought to the room...more tipping expected.
Up to you to decide how to best do the move.