CDC Website (which it looks like you referred to, since you said "adventurous" eating) says:
You can get typhoid through contaminated food or water in Jamaica. CDC recommends this vaccine for most travelers, especially if you are staying with friends or relatives, visiting smaller cities or rural areas, or if you are an adventurous eater.
I would not since you are staying at an all-inclusive. But as another PP said, check with your pediatrician about your kids.