I just did a google search on "Dominican republic" + "metal detecting" + "legal". I see many threads of persons who've taken their detectors there with no issues or problems. Granted, they were all probably beach hunters. So naturally don't raid *obvious historic sensitive monuments* in front of bored archies. But in-so-far as casual beach or something, it appears to be a non-issue.
If you find any key word search hits of someone who found someone to tell them "no", well .... that'd be no different than the USA : If you asked enough bored purist archies, or border lawyer types here too, you'd find someone to screech "no" as well. Because perhaps they're couching the answer in terms of antiquities (spiriting out gold bars across the border), or mel fisher legal hassles, etc.... But in-so-far as casual hobbyist stuff goes, it appears metal detectors are a common site on the beaches there.