The easiest thing to do is for you to drop the family and luggage at the terminal. You pull up to the baggage porters, and they unload your bags. The next time they are seen is in the cabin. Mom then proceeds with kids into the terminal and check in line. Depending on the ages of kids, there is a ship model, characters, cartoons, etc. in the terminal, or they can stand in line with mom. Mom does the check in process for everyone INCLUDING Dad. The CM will hold Dad's KTTW card till he comes in and shows his photo ID, but he won't have to wait in the check in line again.
Dad then goes to return the car and takes the shuttle back to the port. If mom finishes checking in before dad gets back, she gets in the boarding line.
When dad arrives at the port, he finds mom and learns which line has his KTTW. He doesn't have to wait in the whole line again--just wait till the CM finishes with her current guest, then flash his photo ID. She will look at it and hand him his KTTW card. He then joins the rest of the family in the boarding line.
Why is this the best way? First, it gets everyone thru the process faster. Secondly, it is much easier for dad with no luggage to get a place on the shuttle than for a family of 4 with luggage to get on. There's always room for one more, but not for 4 with bags. Finally, the kids would rather watch cartoons than return the car.