Welcome to CruiseMates. We sailed with our kids when they were both over 21, so I can't give much advise regard Circle C. You can often grab a cab and get anywhere you want. Belize is a tender port so you will need to ride a boat (free) into port. You can book excursions through Carnival or search for tour providers on-line. If you rent a car in Mexico get the insurance - you are guilty until proven innocent there.
All I ask is a tall ship and a star to steer her by; John Masefield
Carnival: Glory 2004, Destiny 2008, Splendor 2009, Freedom 2011, Valor 2012, Dream 2013
Celebrity: Summit 2011
Princess: Ruby 2010, 2014, Caribbean 2013, Coral 2014, Regal 2014, 2016, Royal 2017
Star Clippers: Royal Clipper 2015