(Can fit in both post canon and non-canon. Just an idea I had.)
Katara is living at her brother's house in Ba Sing Se, being good friends with Avatar Aang when she receives a surprise- Fire Lord Zuko wants to marry her. She accepts, thinking it will be all right, but she finds out that one of the duties of a Fire Lady is to produce an heir, she becomes uncomfortable with the marriage, added to the fact that she tells her brother "it's not that he's unkind, but he never talks to me". Katara has a child- but a girl, much to the disappointment of her husband, but not to her, and the child is named Ursa. Soon, Aang returns, and her life is happy once more being friends with him. However, one night at a party, she spots her husband talking to Lady Mai. She becomes uncomfortable with this, but after talking to Mai, she confirms that the two of them have nothing going on, and Katara and Mai become friends. Katara is uneasy about Mai's statement that "the Fire Lord must be the only man in the world not in love with his wife". That is soon driven out of her mind by Aang's trouble's with getting some of the politicians to listen to what he's got to say. She says that "I have many faults, not least among them is my ability to draw attention to myself...we could use that to your advantage." She helps him and one night when she's walking home with him, when she asks him if he thinks of her when they're not together, he replies that he thinks of her all the time.

Katara's giddiness is soon trampled with the news that Zuko and Mai have been having an affair. She could put up with practically anything-but not this. Katara wants Mai out of the castle, but Zuko refuses, saying that he's fulfilled his obligations as a spouse, but she hasn't. Katara proposes a deal: she will accept the affair, but he must accept her love for Aang. That drives him to the breaking point, and he says that he couldn't accept that from his wife, and that she must stay till she gives him a son.

Katara begins to become desperate, and one night she says that "I don't understand why women get married, if all husbands are like mine." Soon after, she gives birth to a son, who they name Roku.
Soon, she goes to the Western Air Temple and starts to live with Aang, with Lady Toph Bei Fong encouraging her to be happy. However, Zuko finds out and comes and threatens her with the loss of her children and destroying Aang's reputation. Katara accepts grudgingly. Soon she finds out she's carrying Aang's daughter, and when she's born, names her Kya. Kya is taken to live with Aang, and she finds out who her mother is only after her mother's death at 52.