I would seriously advise against trying to get your parents from Santo Domingo to Las Terrenas during the night, even in a private taxi. The road is quite dangerous at night, and there are a lot of cattle straying onto it, as well as treacherous bends.
I have personally taken taxis at night from LT to SDQ (and vice verca) more than 20 times. The drivers I know have been doing this stretch for years and could probably do it with their eyes closed. They make a pretty gfod living bringing tourist back and forth, are ponctual, and take good care of their vans.
I agree with Steve. I am all for simplifying my vacay and wake up by the beach (but I am spoiled)