I would like to know the name of a movie that a woman lives a life over seas but has another life in the usa.

Passion of Mind (2000) ?

From IMDb: Marty (Demi Moore) is a high-powered single literary agent in Manhattan. Marie (also Moore) is a widow in Provence, France, with two daughters and a peaceful life. Marty has been seeing a therapist (Peter Riegert) to deal with her vivid dreams of Marie's life; when Marie falls asleep, she dreams Marty's life but is much less disturbed by it. Each woman is convinced that the other is a figment of her imagination. When Marty meets Aaron (William Fichtner), they become friends and eventually lovers; terrified that her vivid other life means that she's losing her mind, Marty does not want to tell Aaron about it but finally does. Marie, meanwhile, has met William (Stellan Skarsgård); she, too, is reluctant to tell William about her dreams, particularly since she (as Marty) is falling in love with Aaron~but realizes that she cannot keep such an important part of her life a secret.


https://en.wikipedia.org/wiki/Passion_of_Mind