Vanessa Garcia, now a 37-year-old writer (who is not related to Mr. Garcia), learned the hard way that her mother would take issue with her traveling to Cuba. Back in 2009, taking advantage of the new law that permitted Cuban-Americans with relatives living in Cuba to visit the island, Ms. Garcia bought a plane ticket to Havana with her sister, and then told her mother, Jackie Diaz-Sampol, about the trip they were going to take in a few weeks.

“She got so, so, so red and had a vein popping out of her head,” Ms. Garcia said of her mother, “and she said: ‘I am going to have a heart attack. You are going to kill your mother.’ I tore my tickets, even though we paid $500 for each of them and they were nonrefundable, and threw them down the toilet. I couldn’t do that to my mom.”

Ms. Diaz-Sampol, now 60, said she fretted over the prospect of her daughter going because she worried about her physical safety. “She was naïve, in my opinion, thinking you could go to Cuba like any other country,” she said.

They reached a détente of sorts in 2014, when the mother and daughter traveled back to Cuba together. (And when Ms. Garcia decided to travel to Cuba last May, she hatched a plan to avoid maternal interference: She waited until the night before she left to tell her mother and stepfather of her plans.)

Not all younger Cuban-Americans are eager to visit. For Michelle Marie Arean, a 35-year-old associate editor at Recommend, a travel trade publication based in Miami, the stories she grew up hearing, about government raids of the family home and how her grandfather was exiled to a sugar cane farm where he was abused, were enough to turn her off. “I wouldn’t want to give money and support to a government that took so much away from my family,” she said. She said she would go if the leader is ousted.