We like to use
Budget at Cape Canaveral. They have a free shuttle from the port to the rental location. Just have the driver take the shuttle, have the other two get the luggage.
You can drop off the car at the Doubletree Hotel near Downtown Disney once you have checked in at your hotel. Be aware of the limited hours at the Doubletree location, they close at 5 or 6PM.
In addition, be sure to sign up for Budget's frequent renter program. It's free and will give you priority service at the rental location. Last time, I went ahead of about twenty people!
A one day rental should be less than $40 or so. If you use your American Express card to reserve and pay for your rental use BCD code S208200, for a discounted rate.