Since you have a rental car and to alleviate the stress of yet another long line and having to check the luggage and then wait for it at the other airport--which will also be very busy: can you rearrange your packing so you take only carry on with you to the airport (change of clothes, snacks, etc.) and SHIP everything else home via UPS, FedEx or USPS the night before? If you take enough to get you by a few days you can ship the cheapest method possible. I've had to do this several times. I've even just packed a suitcase and placed the whole suitcase into a box at UPS to send home. And what a joy it was to just drop the car, breeze through the airport past ALL of the curbside and inside people waiting to check bags, hit security and go to the gate.
Also--if you can--print your boarding passes at the hotel or a local place like Kinkos so you can drop the rental and head straight to security?
Here are a few very close places (about 2- 4 miles away) to send packages back home. And don't worry-they sell the boxes and stuff you need! Not super cheap but does your sanity have a price???

And if your airline charges to check bags anyway--well.........
FedEx Kinko's is now
FedEx Office Print & Ship Center
12181 S Apopka Vineland Rd
Orlando, FL 32836
(407) 465-0085
THE UPS STORE
7862 W IRLO BRONSON HWY
KISSIMMEE, FL 34747
407-390-1899
U.S. Post Office
8536 PALM PKWY
ORLANDO, FL 32836-6415
(800) ASK-USPS
Or if onsite can you use that luggage check in at the resort? (Not sure how it works)
HTH.