Names were changed to protect one innocent and a bunch of scumbags, but American Hustle was inspired by the real Operation ABSCAM, in which the FBI used con artist Melvin Weinberg to investigate political figures. Now, he did have a wife in real life, Marie, but she was in truth a dedicated mother and a good woman who felt humiliated by Mel's infidelities and wanted to divorce him. She was essentially the exact opposite of what we saw on screen.
So where did Rosalyn come from? From Mel Weinberg's filthy, lying mouth. After Operation ABSCAM, Weinberg wanted to sell the movie rights to his story. The only problem? He'd surreptitiously pocketed a shitload of cash during ABSCAM, and he didn't want his wife ruining his odds at a film deal (and his prospects for a life outside of prison), so he started threatening her. Marie filed for divorce and went public about Mel's shady dealings, which was the right thing to do. And since this isn't a feel-good Hollywood story, she of course got screwed for it. Mel spread vicious rumors about Marie all around town, hounding her until she eventually hung herself in 1982. In even more depressing news, Marie's death didn't stop Mel from talking shit about her, as he recently referred to her in an interview as a "wacky broad."
Honestly, though, what did you expect from a guy with that haircut and facial hair?