We've never taken any shots before we left on any of our cruises. Only been on 18 Caribbean cruises, but never had any problems. Where are y'all going? Are you planning on drinking water other than bottled water on shore? What are you planning on eating on shore? Best wishes!
You are going to Ocho Rios, Cozumel, Grand Cayman, and Princess Cays. I would not be worried about contracting hepatitis in any of these ports. We've never taken inoculations for a Caribbean cruise, and I've never heard of anyone getting hepatitis while on one.
Please note: Twinrix protects against hepatitis A (infectious through contaminated food and water) and hepatitis B (a ***ually transmitted disease, also infectious through medical, dental and hairdresser's instruments contaminated with blood). Certainly a good idea to get these shots no matter where you go and where you live.