All cruise lines have a Youth service.
Some involve on board activities such as swimmng, volleyball, inside games, movies etc. Some have SCUBA for kids when they stop at port, some cruise lines do day hikes when they dock at port
Carnival Cruise C club for youth. Here is a fine example of what Carnival has.
Taking your kids on a cruise with you is always an excellent idea. Even if your on a second honeymoon, so they get an a-joining room. julie