I've sailed on Western, Eastern and Southern Carribean Cruises (multiple times). My favorite is the Eastern Carribean (save southern for the winter months & it's more expensive).
All have families and kids running around...fewer on the highend lines (Celebrity) but I think Carnival has more because they tend to be cheaper and families can afford it. There is more of a Las Vegas style show on Carnival if you prefer that and a lot of "spring break" atmosphere along with greater numbers of the 20 something crowd. I prefer Norwegian or Royal Carribean, as they have a broader mix and better quality shows (less raunchy). Sailing on my first Princess cruise this summer (to alaska).
You'll have fun no matter what...if you visit the carribean!