My version:
Castro drowns as a young man. Later, a pro-American democratic movement overthrows Batista in 1957. Dominican communists do not have an uprising in '59, but focus on building revolutionary infrastructure in the unions.
1959- Francois Duvalier dies of a heart attack. Haiti descends into a period of turmoil.
1960- Butterflies on the campaign trail and a marital scandal for Nelson Rockefeller help lead to a Nixon victory.
1960- Betancourt assassination fails, but assassins are still caught. The uninjured Betancourt uses the attempt to shame Trujillo in the eyes of the world, and to bolster himself. Butterflies mean that only two of the Hermanas Mirabal- Patria and Minerva- are attacked in early December, 1960. Dede and Maria Teresa survive by virtue of not being present.
1961- Trujillo badly injured, but not killed, in his own assassination. He is heavily weakened, and the broad opposition sees opportunity amidst a weak economy and a weakened Caudillo. Uprisings begin in the less-populated north, and urban riots shake Santo Domingo.
The United States, hoping to prevent similar uprisings in Haiti, seize Samana Bay and then temporarily occupy Haiti to restore order. A black general is given the reins of power in order to stabilize Haiti.
In the Dominican Republic, Trujillo forces continue to be defeated by rebels, in part thanks to desertions. Trujillo by this point is barely lucid, although he is slowly recovering.
In mid-February 1962, Santo Domingo, which had been a Trujillo stronghold after the defeat of rioters, is seized. By this point, Trujillo is once again lucid, just in time to see rebels destroy the entire edifice of his government. In a public ceremony on Valentines Day, a large ceremony takes place. Trujillo, most of his family (i.e. those who had not escaped), and much of his governing ministers are executed by gunshots to the back of the head. The United States has occupied major naval bases, but had been unable and largely unwilling to support the unpopular and increasingly crazy Trujillo. A new Dominican Republic is declared. The leader of the revolution had previously promised to be anti-Communist; instead, he declares the People's Dominican Republic. Nixon considers invading, but Soviet recognition of the new state and concerns elsewhere abroad lead him to take the cautious route. Hardware is sold to Haiti, and military installations are created in Western Puerto Rico. As Trujilloist counter-rebellions fade, the US bombs most of the industrial infrastructure before retreating back to their well-armed bases.
1962-1993: The PDR joins the Soviet bloc, although American seizure of major bases prevents the country from having any major military significance to the Russians. The Haitian dictatorship stands as a solid counterbalance to the PDR, even as it is led by a general who apes the image of Baron Samedi and tortures left-wing dissidents. Cuba, capitalist and thoroughly American, remains the richest economy in the Caribbean as democracy takes hold in the society there. Puerto Rico is more developed militarily, but is still not a state. Nixon leaves office after a successful term in office, even with some limited student troubles relating to proxy wars abroad (Vietnam doesn't happen, largely because a successful offensive and uprising against Diem come about before major US support materializes. A rump South Vietnam in what was Cochinchina is preserved, with capital at Saigon).
In 1993, the Soviet Union finally falls, after the 1989 German reunification and the short North Korean Civil War (upon the death of Kim il-Sung in 1991)/Korean Reunification. Russia manages to hold on to Ukraine, Belarus and small regions of the Baltics and Kazakhstan under a broadly nationalist-military government. The Soviet Union is replaced by the Eurasian Commonwealth.
The PDR, without Soviet subsidies and led by a gerontocratic oligarchy, begins to suffer. The economy tanks, and with the fall of the Haitian regime in 1998 the Communists no longer have a convenient boogeyman with which to intimidate people. In 2006, pro-democratic riots break out in Santo Domingo, consuming the island entirely. The PDR falls, and is replaced with the Dominican Republic. Foreign aid to anti-communist regimes in Haiti, and capitalist development in Cuba and other places, have left the DR the poorest country in the Caribbean, even more so than Haiti. The 2008 elections are heavily corrupt, and a broadly left-wing but non-Communist general mounts a coup in order to take over. The DR is democratic in name, but largely run by the Officers Movement.