The least expensive tends to be a one way car rental from the airport to Cape Canaveral where most of the majors have offices with a shuttle service from there to the pier (but chk...not ALL have shuttles)
Dad can drop mom and kids at the terminal - with the documents - and while dad returns the car and takes shuttle back, mom checks in. By the time dad gets there you walk on board ....
Many couple this with a day early arrival - for stress reduction - and a nite in Cape Canaveral / Cocoa Beach.
With one of the zillions of discounts out there, a one way one day car rental can be very cost effective. The drive is EASY - the airport to the port/Cape Canaveral is a straight shot.... And only about 45 miles so gas isn't a concern. One toll $1.25.
But that same 45 miles make a taxi out of the question and shuttles have their good ones and their bad ones.....
Right now I believe Hertz location wins the closest to the
DCL pier contest...but the real estate wars continue!
p.s. when checking companies...you want a location in Cape Canaveral or Cocoa Beach. Port Canaveral is not a 'town' and there is no rental agency with that address.