This could also be Code 46.
It features a relationship between a man and the clone of his mother.
Society is regulated by various "codes". The code of the movie title prohibits "genetically incestuous reproduction", which may occur as a result of the various medical technologies which have become commonplace, such as cloning.
William Geld (Tim Robbins), an insurance fraud investigator, is sent to Shanghai to interview employees at a company known as "The Sphinx", which manufactures "covers", ostensibly "insurance cover documents" but which in fact regulate the movements of people among cities and "inside" and "outside". William's assignment is to identify employees who are suspected of forging "covers". After interviewing numerous Sphinx employees, he identifies a young worker named Maria Gonzalez (Samantha Morton) as the forger.
He falls for Maria and has a fling, only to later discover:
Upon his return William discovers that Maria has gone. Her apartment is abandoned and the only clue is a medical clinic appointment. He visits the clinic and, using his empathic abilities, learns that Maria was pregnant, but that it was terminated due to a violation of Code 46. William knows that this means Maria is somehow genetically related to him, but he has no idea how.
William discovers that Maria has been taken to have her memory of the episode erased. He talks to Maria, but finds her memory of him is gone. He succeeds in getting the clinic to release Maria into his care by telling them she is a witness in his fraud investigation. After she is released, William proves to Maria that she knows him by his intimate knowledge of her and by showing her the memory recording of when she gave Damian the papelle, which includes a shot of William. William tells her about the memory erasure, and about how he didn't report her for fraud. Maria is disturbed by this information and becomes very distressed. William gives her a sleeping pill and, while she is sleeping, he cuts some hair from her head and takes it to a facility which provides instant DNA analysis. There he discovers that Maria is fifty percent genetically related to him, and that she is a biological clone of his mother, who was one of a set of twenty-four in-vitro fertilised clones. This knowledge does not affect William's feelings, but instead of going back to Maria he decides to go home to his family. However, when he tries to leave he is not allowed to do so as his 24-hour cover is now expired.
He goes back to her for help, then she starts to remember her feelings for him, and they run off together, only to have the government find out about it again, and she's punished by banishment while he has his memories erased. This might account for what you remember of "other versions" of them.