Kelley was also a good friend with Petraeus’s wife so why would she turn the FBI onto Petraeus’s wife? If Kelley thought it was his wife, she would have at least showed or told Petraeus about the email and let him figure it out and take care of it. I’m mean we are talking about the soldier/General of the century here, not a whuss!
She might have just decided she didn't want to worry Petraeus.
Kelley may not have gone to Petraeus because she found out about the affair and wanted to expose him. So she sent the threatening emails to herself to get the FBI involved so they would discover the affair. At this point most anything is possible.