au + 5 hc- Toph and Zuko marry for political reasons, and now their children have to deal with the political consenquences
1. The avatar did not awaken. Instead, the Earth Kingdom army and the Northern Water Tribe invaded on the Day of Black Sun and overthrew Ozai. Zuko’s ship was captured soon after, and Iroh put in prison. Zuko was put on the throne as a puppet monarch. Zuko has not had his redemption/recovery arc, so he is still a hostile snarly, anxious unhappy twerp, only now Ozai is dead, and Zuko is free to lionize him without having to face the reality of who Ozai really was. Also Iroh is in prison in the Earth Kingdom awaiting execution, and Azula is running around making everything about a hundred times more difficult.
2. Azula makes a bid for the throne, persuading a group of Dai Li and disgruntled Fire nobles to back her. At the same time, Iroh escapes and makes his way home. Somehow this ends with Zuko still on the throne, Iroh safe, and the Dai Li at least out of Zuko’s court. But the other upshot is that Zuko needs to marry an Earth Kingdom noble in order to prevent another invasion. The Bei Fongs manage to luck out as the family to garner the most backers in he Earth Kingdom, so their thirteen-year-old daughter is escorted to the Fire Nation by her mother and several regiments of the Earth Kingdom army.
3. Zuko takes one look at her and marries her just to get her away from the people who are willing to marry her off at thirteen. Consummation of this marriage is not going to happen for a looooong time. But Toph might be a frightened child, but she would never let that show. She keeps running away. Not back to her parents as might be expected, just away, to the wilds of the Fire Nation, to the inner city, anywhere she can get to. She bends the glass out of her windows, she tears up Zuko’s mother’s garden, the only person who can really get her to do anything is Iroh, and now he has two intractable, bad tempered teens to look after, and Zuko is now even less willing to listen to him now that he’s got a crown.
4. Eventually, the two of them settle into a siblingish relationship, and Toph eventually grows up to realize no body here really has a choice, so she’s going to have to just deal. She still absolutely despises everything involved with being Firelady. Also Zuko resurrected the prewar custom of official concubinage when Mai accidentally got pregnant, and Toph is careful only to take firebenders as lovers.
5. Doesn’t matter. Both her children are earthbenders, even Lin, who is actually Zuko’s. Izumi, his acknowledged bastard, has to take the throne. The mess that is the royal inheritance at this time very nearly touches off a civil war, and a couple of islands do break away and declare Lin their queen. Lin has to go down there to knock some sense into them.