In the late 1950s, Trapani's organization supported Michael Corleone's dealings in Cuba with Hyman Roth and the government of Fulgencio Batista. Aldo Trapani and Dominic Corleone made frequent business trips to Havana and were also present at the meeting in late 1958, to celebrate Roth's birthday and to get a piece of his operations. However, after the meeting, president Batista declared his abdication after his forces were defeated by the rebels of Fidel Castro, forcing Michael Corleone, Aldo Trapani and Dominic to flee the country. During a raid by the rebels, Aldo Trapani was killed while arriving at Havana's airport. Shortly after, Michael Corleone made Dominic the new Don of the Trapani crime family.
Back in New York, Dominic was informed that some of his own men joined forces with the Rosato Brothers, who were two former caporegimes who had started their own families, causing an uproar in the criminal underworld. Dominic was given instructions to deal with the matter, and after killing Carmine Rosato and his men, he was called to Florida to help Hyman Roth's organization and to set up new businesses. Under Dominic's ambitious reign the Trapani family expanded quickly, recruiting new men and forming a partnership with Roth and the Manganos. They also started working together with the CIA via their agent Henry Mitchell, who gave information about the status in Cuba. New wars where fought for supremacy with the Almeidas in Cuba and the Granados from Mexico, which were all won. After the assassination of Hyman Roth, Dominic had conquered the position of boss of the Corleone crime family, given way from Michael Corleone, doing flow into Trapani crime family in the Corleone crime family.