Jet Blue's Secret of Sucess
You're kidding? What do they do ? rent other airlines planes when everyone is sleeping? Why would they schedule such peculiar hours for a 3 hour flight?
I have arrived at about 5:20am, and had to wake up the immigration guy and saw nobody outside in car rentals or taxis even at that time, 2 a.m. seems iffy.
You might want to arrange a taxi in advance and a hotel (or a cabana RD$300 or so for 4 hours) or something nearby like Boca Chica and do this later on. Returning sounds like a pain also. Where (city) are you staying?