Sounds like you picked up something from either the tap water or perhaps something with ice in it? A lot of times travelers forget about the water in the ice cubes. Also whatever was in the water your food was washed in. I suppose it could be the fish as well, or general food handling techniques. It really doesn't mean for sure that anything was done badly or in a non-hygienic way - you just have immunity to the bacteria in your own area of the US and not to anything they have in Punta Cana. Everyone there is drinking the water and doing fine because they have some immunity built up.
I don't think this was just a "change of food" issue - it really sounds like a bacterial/lower GI bug. It should resolve itself - use the BRAT diet to control diarrhea: bananas, rice, applesauce, toast (or turkey). No roughage or fiber for the moment. Probiotics in yogurt can add some good bacteria back to your gut if you can handle the dairy products. Cheese helps bind you up too. Just don't go overboard and wind up constipated, you know?
And hydrate hydrate hydrate. You and your daughter are losing fluids daily. The electrolyte stuff you buy in the store is not great, and plain water may not be enough. DO NOT do Gatorade or Power Ade or Vitamin Water or any of that stuff! Too many artificial dyes which aren't good for you anyway but also can be irritants, which you definitely don't need now. Some of them are under investigation anyway for making health claims. You can buy something on line that I can recommend but it will take a few days to get to you. Depends how sick you are and whether you want something for regular use. I have a family of athletes and we use it all the time.