"Can we rent a car once we have arrived at our resort in Disney World? What I mean, can we decide once we are at the hotel that we would like a car for a few days and then could they arrange for us to rent one?"
Well, that's an easy one. Yeah, you can, absolutely. There's several ways you can do it. The easiest way is Disney has their Car Care Center, which is just south of the Magic Kingdom. the Disney Car Care Center, will help you if you have problems with your car.
Also in the Car Care Center there are two rental agencies, Alamo and National. Both have rental cars available. You can make arrangements with them, they will come to your hotel and pick you up, take you to the Car Care Center where you can rent the car.
You bring it back to the rental car center or you take it back to the airport, however you set it up.
You can pick them up there, you can take them back there, and they'll transport you back and forth to your hotel. It's just that Simple.
Dad's bottom line, Disney makes it easy. All you have to do is get in touch with the Car Care Center or National or Alamo. You can do it directly with National and Alamo and set it to pick it up at the Disney Car Care Center.
There are a couple of other rental locations around Walt Disney World, especially over in the Disney Springs area. But the Car Care Center is probably the easiest.