During the course of The Godfather Michael marries Appolonia in Sicily. A failed assasination attempt results in her death. Shortly after, Michael returns to New York and marries Kay Adams. There was no mention of Appolonia in the rest of the Godfather trilogy apart from a deleted scene where her killer was murdered by a car bomb and a flashback at the end of 3. Did anyone back in America know of the marriage?
In the film, this was never revealed. In the book, Kay is told by Michael Corleone's mother to forget about him, implying that Corleone was already married and would never return to the US. The family in the novel The Godfather is well aware of Michael's actions in Sicily.
Since the film leaves out Michael Corleone's revenge against the man who planted the bomb in the car which killed Apollonia it is clear that her death closes that thread of the tale.
In The Godfather 3, a wise and aged Michael Corleone shows a photo of Apollonia to his daughter Mary and his son Anthony saying
She was wonderful, beautiful. I loved her. And then she died. My trusted bodyguard planted a bomb in my car. She drove it before I did.
The idea behind this conversation was to convince Mary to stop her relationship with Vincent Mancini, the illegitimate son of Sonny Corleone and Lucy Mancini.
When they come... they come at what you love.