The S.S. Andania, plain and sturdy, pulled into New York Harbor on April 11, 1923, after a slow journey from Liverpool, England. In a third-class cabin was a gray-eyed Irishman named Richard Michael Cawley, fleeing poverty and war.

The son of a tailor from a rural village, Mr. Cawley, then 20, had come of age during a guerrilla conflict. Now, with Irish fighting Irish, he had made his way to America to join his older brother and uncle.

He would settle in Chicago, a city bursting with Irish Roman Catholic life; marry a teacher; find work as a streetcar driver; and sing ballads by the piano on Saturday nights. He would become an American citizen, march in St. Patrick’s Day parades and visit Ireland, looking, one cousin marveled, like “a real Yank.”

It is a familiar American tale, except for this: Mr. Cawley’s grandson and namesake, Michael Richard Pence, is the vice president of the United States, which is in the thick of a roiling immigration debate.