Leni,
Welcome to Cruisemates!!!
It is true that Jamaica can be a little scary, but if you stick with one of Carnivals excursions, you should feel more protected.
Tell me if all of you are able to get around okay. If you can, I would suggest climbing the falls. I think everyone should do it at least once.
There is so much to do in Coz. Go to the Carnival web site. Look at the excursions, and pick out a couple that sound good to you. I have done them all, so I will be able to answer your questions.