Ozai/Zhao/Yue love triangle, except Yue may or may not be jealous whenever Zhao is around Ozai.
Yue knows she shouldn't care about how Zhao acts around the Firelord. One had gotten her into this mess in the first place, a marriage to secure the "alliance" between her tribe and the Fire Nation, and the other had been the one to officiate the ceremony.
And she doesn't care about it- for the first few months she's glad the admiral's attention lies elsewhere. It's only over time that her sentiments slowly start to shift.
Something about how Zhao seems to metaphorically drop everything the moment the Firelord is mentioned, when he bows longer than necessary before Ozai, and when he addresses him as "My lord", "My liege" with a tone a little too revering... it begins to frustrate Yue.
It doesn't help that she can't quite point a finger on whether or not the relationship of the two had actually ever gone beyond what would be considered appropriate – Ozai never appears to be bothered by it, despite being generally contemptuous otherwise – or if it's nothing more than woefully one-sided.
Ozai, by then, has taken notice of Yue's irritation. She might've been able to hide it expertly from others (Zhao certainly has no clue), as she had been born into and raised as royalty, as well, but he still has more than twice as much experience to show for and grew up in an environment significantly more competitive than hers.
And what does he do about it? Ozai, bored by the lull following the acquisition of the Northern Water Tribe, decides to play and have a little fun...with both of them.