Car services charge anywhere between $180.00 to $230.00 round trip to the port. There are threads about renting a car that you can check out. Disney (even the other lines) will get you over there for $210.00 (3 persons). I am told they all charge $70.00 round trip, but have not verified it. You would take the hotel shuttle back to the airport and go to a central spot to catch a bus to the port.
A car service will pick you up at the hotel, carry you to the port, provide baby seats if you have youngsters, stop at a grocery store, drug store or liquor store for extra items and be at the port when you disembark to get you straight back to MCO. The service can't be beat by any other other transportation alternative.
There are numerous hotels at the airport that you could stay at. Here are a few. Amerisuites (2), Raddison, Renaissance, Hampton Inn, Embassy, Marriot Airport (expensive one), Marriott Courtyard and Hilton Gardens. A car service will pick you up at any one of these and many more unnamed and take you to the port. There is a Hyatt in the airport and the concierge could help you find a transfer to the port.