I'm heading there too this summer. I saw photos taken from a tripadvisor and asked the guy if he had any issues. This was his response:
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I had no issues at all. I have the DJI hardshell backpack so I took it as carry-on. They checked nothing at customs in either direction. On the way out, they asked me to open it at the airport security after x-ray, once they saw it they were satisfied. At the resort I was very careful not to fly it from the crowded beach area. I would walk down past the resort and launch it. The beaches are "federal property" and not owned by the resort. Once airborne it could not be heard or seen once above about 50'. There was once time when I was flying about 30' down from the resort over the ocean and a very low flying helicopter went by between me and the drone. It was about 100' out from the beach and the helo was flying right at the beach break. Scared the hell out of me, but it is an amazing video. All the other helicopters were flying about 200' up and about 1000' out. I think this one may have seen the drone and purposely buzzed it.
Security at the beach had no issues other than their own interest in it. I took it to Catalina Island and flew it off the beach. There was a policeman at the beach who was very interested and watched. I was very respectful of people on the beach and on the resort, I did not want to create a problem for myself or future quadcopter operators. My Phantom is registered with the FAA as required in the US and I laminated the card and kept it in the case. It is and looks official and I think it would help to show it if questioned. One Dominican told me that the DR also has a registration requirement. I would think that they would honor ours just like they honor all aircraft registrations. You don't need to register you airplane in the DR to fly it there.
If asked, I refer to the phantom 3 as camera equipment, because basically the entire drone is to carry the camera.
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Hope that helps.