Hi Jenny:
I'm the family cruise editor here. We've been on the Adventure of the Seas -- Navigator is a similar ship -- and my 9 year old loved it! Your kids are great ages for these ships since there are so many active things to do -- rock walls, in line skating, ice rink, etc. Royal Caribbean has a great youth program too.
What's even better is that Navigator has the largest teen facilities at sea. Your 14 year old will have plenty of teens to hang out with in "cool" places -- a coffee house style room, an internet cafe, teen deck area, etc. I'd love to hear how your teen in particular enjoyed the cruise and new facilities once you return.
Smooth sailing!
Luisa Frey Gaynor