I drove here with my expired US license for almost a year, now I decided to get a DR license, which is pretty easy, especially if you speak a little Spanish. I have stopped few times in a police check point by the Policia Nacional, and when they asked my papers I just told them my papers are fine and that was it. They never demanded to see them, they never searched my car either after I was telling them that I have no guns. My expired DL worked everywhere when I had to identified myself - even though I have residency - I wanted to see if I can get away with it.
I guess maybe 30% or more of the Dominican drivers has no license at all. I know many who owns a car and drives regularly without a license and I was told by them that they -being Dominicans- would be in bigger trouble if the police stops them.
The police here have no computers in their car, so there is no way to run a check on anyone, especially on a foreigner.
That's true if you have an accident without a valid license you are in trouble. BUT, even with a valid US license you can drive only 2 or 3 months here legally.
Sometimes the best way is to play the stupid gringo who doesn't speak a word of spanish, just give them your license and smile.
NEVER, EVER give your passport to anyone at a traffic stop, get a certified copy from a lawyer or a notary and carry that, or least give that if they insist. Tell them your real one is locked in the hotel's safe...
BTW, when I came to the DR I was renting a car at the airport from Sixt and they didn't even asked my DL, only took a copy of my passport.
And yes, if you want to cover your a$$, get a DR license as soon as you have your residency.
The Hun