Is “An other-other woman (person / thing)” a popular English phrase?

Solution 1:

When a married man has an affair with a single woman, that woman is sometimes referred to as "the Other Woman." Perhaps that phrase could be regarded as slang, but it's well established in literature, even in relationship counseling. (For example, see this book, this book, or a host of others.)

Jealousy rages in exposed extramarital affairs; the wife may be angry at (and jealous of) the Other Woman, yet the Other Woman might feel jealousy toward the wife, too (because the wife is able to show her affection in public, for example). The term Other Woman often functions as a "pronoun" of sorts when describing such emotions in the general case.

I haven't been following the lurid details of the Petraeus case, but, from what bits I've seen, I think he was intimate with two other women. Dowd's way of commenting on this juicy scandal, then, is to refer to the other other woman, in other words, the woman whom Petraeus had an affair with, after Petraeus was already having an affair.

At some point in time, the Other Woman may have become aware of Petraeus’ indiscretions with the Other Other Woman (or vice-versa) – at least that's what I'd assume from Dowd's account, since the expression Other Woman is often used when sorting out the emotional aftermath of an exposed affair. But I could be wrong about that, and Ms. Dowd may just be piling on with dramatic words, as she is often wont to do.

To answer your last question, no, the expression other other woman isn't all that common – partly because Ms. Dowd probably injected that over-the-top phrase in her colorful paragraph to evoke titillated chuckles and scandalous gasps (along with "toned arms, slinky outfits, a cat fight", etc.), and partly because similarly-structured relationships between four people seldom get so much press.

Your question has made me curious, though: perhaps ELU has tainted me somewhat. Instead of being tempted to go learn more about the sultry Petraeus affairs, I'm left wondering if Ms. Dowd correctly hyphenated other-other woman.

Solution 2:

A married man's mistress is often referred to as the other woman. Since the Petraeus scandal involves a second mistress, she is — for added effect — being referred to as the other-other woman.

I agree with @J.R. that the phrase is incorrectly hyphenated. If it needed to be hyphenated at all, it should have been the other other-woman instead.

Seeing as to how other woman has warranted a dictionary entry of its own, it's a recognised phrase. Authors also like exercising a little licence and introducing wordplay into their writing; this is what Dowd has done with other-other woman. Using alternatives (such as another or separate) that did not plainly involve this phrase would not have meant the same thing.