Definitely drop off the luggages and everyone except the driver at the port first. The rental car shuttles can be very crowded and may not fit your entire group and all your luggages. Also, loading and unloading the luggages multiple times will be tiring in the hot, humid Florida weather. The earlier drop off will also let you get in the boarding line quicker. You can check in everyone without the driver. They'll hold the driver's KTTW card until he/she arrives back to the terminal.
Another option after dropping off luggages is for you to park the rental car at the free short-term lot across the main street. You can then check-in, board the ship, and have lunch first all together. When you're settled into your cabin, you can send the driver back to return the rental car at his/her leisure. Just don't forget to do so before the rental agency closes. For
Avis, I think it's 3 PM. Also, make sure you allow enough time to take the shuttle back to the ship before it departs.
