Ipersonally think that a parliamentary system would work better in the Dominican Republic.
The head of state would a be a president, elected by all the people, but his duties would be mostly symbolic, a symbol of unity, something like the president of Germany.
The head of government would be elected by the majority in parliament and his government would be subject to keeping a working mayority.
This arrangement would solve one big problem: you could criticize the head of government without criticizing the head of state. I've noticed in the DR they have been hauling people to jail for their comments towards the president. Since in a parliamentary system, the president would basically cut ribbons there is nothing to criticize, thus no insults, save the dresses his wife buys, that kid of silly thing.