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Face/Off is a blockbuster science fiction action thriller from John Woo and the film stars John Travolta as a vengeful FBI agent whom goes undercover as his nemesis, a comatose sadistic terrorist (Nicola Cage) when he undergoes a face transplant, allowing him to assume his nemesis's identity and goes to the hi-tech prison where his nemesis's brother is imprisoned and to find out the location of a bomb that his nemesis hid somewhere in Los Angeles, before it detonates in 72 hours. Edit
Because Castor was planning on using the FBI to eliminate Dietrich and his gang so that Castor could sever ties with him.
Plus Dietrich was more of an associate who Castor occasionally did business with and not a partner. Castor more than likely had numerous associates across several major US cities so unless he was ready to do business with any of them once again there was no reason to tell everyone he knew about the switch. That was probably Archer's line of thinking when he infiltrated Dietrich's gang and how he knew his cover wasn't blown. Edit
It's hard to say however it's apparent that she realized that something wasn't right. It was definitely strange that the man who looked like Sean Archer was pointing a gun at his own wife and the man who looked like Castor Troy was pointing a gun at his two bodyguards. Even if she did figure it out she obviously chose to side with Archer (that is, Archer-as-Castor). Even though she hated Archer for threatening to take her son away for refusing to give up information about Castor, she hated Castor even more for walking out on her and Adam, and for the evil person he had become. Furthermore she knew that the man who looked like Archer was the one who shot her brother Dietrich, and Archer-as-Castor had opened up to her and shown genuine concern for her son, probably the only person in her life who had ever done so.
Furthermore when she said "take care of our boy" she may have very well considered Archer to be more of a father to Adam than Castor could ever be, so the fact that she referred to Adam as "our boy" doesn't necessarily mean that she was oblivious to the switch. Edit