In a nutshell: A convict streals his cellmate’s identity, visits his (cellmate’s) biological mother which has abandoned him as a child because she couldn’t take care of him and pretends she is HIS biological mother and that he’s been looking for her. Then, after he convinced her he’s her son he is invited to live with her (and her husband and teenaged foster daughter). He eventually kills the husband (I believe with a syringe with a untraceable poison) and he makes his crazy girlfriend hold the daughter hostage with a gun while he forces the mother to take a big load of money from the bank. The ending is a bit fuzzy, though. I’m not sure if the convicts both die at the end. Anyway, at the very end the mother and the daughter meet the REAL son as he walks out of prison and she gives him a hug at the last frame.
The movie you are thinking of might be called “Unforgettable” (1996), directed by John Dahl and starring Ray Liotta, Linda Fiorentino, and Peter Coyote.
Stranger at the Door (TV Movie 2004)