Suggestion - go to hotel and drop off all luggage and passengers.
Drive to Alamo and the shuttle/AirTran is easier with only one person. It isn't that bad but as mention but can add each 15 minutes at each junction and you have 3 (AirTran > AirTran > Hotel shuttle). If you are press for time you can drive to 7-11 (on airport) or taxi queue at any terminal and ask a taxi driver to follow you to Alamo so you have a cab but not worth the cost if you can do it for free with a little time.