Elsa's account of the conversation between Amyas and Caroline in the library - the one in which Caroline says "You and your women!" - was a lie. Are we to assume that Elsa was not called to recount that conversation at Caroline's trial? If she had, Caroline would have smelled a rat immediately.
I think the implication was that it was real- it was also when Caroline said: "I'll kill you one of these days!" The actual words did incriminate her, but only because Elsa drastically changed the manner in which they were spoken to sound furious and threatening, rather than affectionately exasperated.
While Elsa did lie to Poirot about hearing Amyas say he was going to leave Caroline, this part was probably invented for Poirot in particular. All she had to do at trial was recount the parts that were actually said, and Caroline would think nothing of Elsa mishearing the intent behind the words.
It seems as though Poirot missed the opportunity for an Engineered Public Confession at the end. Why did he not secretly bring officers or other witnesses to overhear his private conversation with Elsa?
He knows that it would be futile because even if Elsa were incriminated, her husband would get her off the hook, since she's of high class now and the case is more than ten years old. He even mentions this at the end, but knows that Elsa has trouble living with herself.
Also, he couldn't have known for sure that Elsa would decide to have a private conversation with him (it was Elsa's decision to start it).