We haven't done any vaccinations for our DD (4 in Oct) since she was 4mo. We are going on a cruise in September with stops in Haiti, Mexico and Jamaica. DH is freaking out that she isn't vaccinated and wants to do some to prevent disease that he is worried she'll be exposed to on the ship and islands. Clearly I'm anti-vax and he is more pro (though willing to be selective and delay, obviously). I don't want to expose her to something that may actually kill her or cause irrevocable damage, but I don't want to suddenly jump on the vax ride, either.
Taking our non-vax (mostly) DD on a cruise in September - DH wants to vax.
Looking at this schedule (http://www.cdc.gov/vaccines/parents/downloads/parent-ver-sch-0-6yrs.pdf), I think you're saying your daughter had 2 shots each of Hep B, Rotavirius, DTaP, PCV and IPV. She's "missed" boosters for all of those, so the immunity she gained may have dropped, I don't know how much of an effect that is - others on here (or your doctor!) would be better sources.
In addition she's had no shots for varicella, influenza, MMR, or Hep A.
Looking at the ones she's not had at all:
My guess flu not a big deal in the summer/early autumn. Chicken pox would be a nuisance (and the cruise ship might not let you on if she shows spots - I know airlines have that rule as we had a CP scare right before an international flight - turned out to not be CP), but most likely not serious if she's healthy.
Mexico appears on this map: http://wwwnc.cdc.gov/travel/yellowbook/2012/chapter-3-infectious-diseases-related-to-travel/hepatitis-a.htm#2394 as an intermediate risk country for HepA. So this does seem like a plausible concern to me.
There is a measles note from the CDC over several countries (from which travellers on the ship with you may have come, although not specifically noted in Central America/Caribean)
To my mind this is the one I'd be most concerned about, and if I were to get a single shot for her it would be MMR (or separate Measles if you can get it). I know very little about mumps if I'm honest (except that I had it as a child). I think rubella is usually quite mild in children (just can have tragic consequences if they transmit it to a pregnant women who's not protected). So in terms of your daughters health it's only measles I'd be concerned about.
Anyway just some thoughts from me. Hope it's helpful in your decision.
I would look at the prevalence of VPD's in ports of call.
Here is a map I found to get you started.
In all probability you will be back home before any disease pops up in the unlikely event you get something, so that is good.
I imagine you will only be off the ship for a few hours at a time, and will most likely be sightseeing/doing excursions. I think there is fairly little chance you will catch anything from locals at ports-of-call.
I did have an internal debate with myself on Hep shots when I went to Cuba for a week. I did decide against it, but know people who got Hep A and B (twinrix?) shots. I would research Hep A - here is a vaccine-questionning site to get you started:
Here is what the CDC has to say:
Have a great trip - and I hope you and DH come to an informed agreement you both can support!