Another option is to stay at the Hyatt in the middle of the MCO terminal and you can just walk to pick up your car.
You can ask the driver to drop you off at MCO. However, keep in mind that the airport is divided into 2 "side" A and B side. They should send you an email saying which side your car will be. If you don't know an arrival airline, most often they give you a car from the A side.