You should not discount the travelers advice either. Sometimes residents (locals)view things a little less important and do not understand how the difference in living standards can affect a vacation.
That being said, my wife and I have been to both islands and the mainland many times. CC is a wonderful village with the most laid back people who are welcoming and friendly. AC has more activities, but also more visitors (not crowded though) There is obviously more to explore on AC because it is so much bigger. The mainland is yet another world alltogether. Beautiful and undeveloped (except a few cities). You must take precautions anywhere you go. We have never had any medical issues or felt unsafe, but we take precautions. We don't stagger around drunk at 2 in the morning, waving our wallets. I don't know what your kids enjoy, but have heard from many travelers that AC is more to the younger ones liking.
You are doing the right thing by asking questions. Relax, you will love this trip and plan another right after returning.

Play, Love, Share and Enjoy - it doesn't last forever make sure you get the most out of it.