Disclaimer: Yep, Avatar belongs to the creators, all that. Not me.
Mother
Sometimes, when Mai is long asleep and the palace is quiet, Zuko pulls a hood over his face and takes Izumi's hand. Her steps are quiet and her face impassive, as if the Blue Spirit himself had trained her. They arrive at the house by the sea just as the sun breaks over the horizon and colors the sky with reds and golds that reflect over the water. It draws a woman out of the shadowed shack that stands out against the sand like a spot of ink on clean parchment. Zuko says the same thing he always does when he offers to build something better, and the woman says the same thing she always does when she refuses him with a vicious mockery that has long lost its force and sting. Izumi kneels in the sand at the woman's feet where she stands, planted in the sand with a posture that ought to be regal but isn't quite straight and isn't quite proud.
"Happy Birthday, Mother."
"Don't call me that."
"What will you have me call you?" Izumi is always careful to be deferent and formal; Mother prefers it and Father (Uncle) advises that it is best to let Mother come to terms with things in her own time.
"Fire Lord Azula."
And then, sometimes, when Zuko has turned to walk down the beach and stare at the water as if it's the most fascinating thing in the world, Azula sinks to her knees beside her daughter and asks whether she's been keeping up her firebending training. Izumi's fingers spark with cold fire for a moment and for that moment Azula's smile is pure, unbroken, and, sometimes, straight and proud.
AN:
Sometimes I like to toy with the idea that Izumi is actually Azula's daughter that Zuko adopted (though how Azula ended up with a baby is something I haven't quite figured out yet, the obvious aside). The contingencies give me a headache though, so I'll just leave this here as is.