Azulon arranges the marriage of Ursa and Ozai to combine the bloodlines of the Fire Nation royal family and Avatar Roku to produce a more powerful heir. But we know from "Zuko Alone" that Azulon favored Iroh and didn't want Ozai to succeed him. Why bother with such eugenics on what you intend to be the Spare branch of your family? That part could be explained if Iroh's wife was still alive at that point, so, to put it another way, this whole exchange makes it seem like Azulon intends Ozai's descendants to be his heirs, but we know that he was adamant that Iroh would succeed him.
This has been mentioned on the WMG page, but Azulon was not impressed by Zuko's firebending abilities at all, and likely regarded him as a sort of failure. He took the first chance he could at simply killing him off, opening up the throne to his experiment's successful result, Azula. Perhaps Azulon was more successful in getting rid of Lu Ten, who might have already shown just how talented at firebending he was by the time Ozai and Ursa were engaged/married. The Fire Sages told him that combining Roku's genes with Fire Nation genes would produce a powerful heir, but there was a problem: Iroh didn't want to remarry and try having more children in his forties or fifties, and even then Lu Ten would be in the way of that child inheriting the throne. So Azulon got Ozai and Ursa engaged, pressured Lu Ten to join the Fire Nation army, kept Ozai safe in the castle on the off-chance that Iroh and/or Lu Ten were killed in battle, then did something strategically impossible/pointless to get Lu Ten and/or Iroh killed so Ozai and his more powerful heirs could inherit the throne.
According to Ozai, Zuko didn't truly display the spark of firebending when he was born, so much so that Ozai considered to throw him out in shame of having a non-bender be his firstborn if it weren't the persuasion of Ursa and the Fire Sages. Given that Zuko is heir to Ozai's bloodline, Azulon wouldn't be happy if this where the Fire Lord's lineage is heading.
Iroh had no heirs, which means the thrones would have been given to Zuko or Azula eventually. there was no reason why Iroh could not be the heir and still give the throne to his nephew or niece other than Ozais desire for power. Azulon may have been sincere in his desire not to betray Iroh after his own son had been killed in the war.
Lu Ten hadn't died yet when Ozai and Ursa's marriage was arranged, and since he was older than Zuko, old enough to be a soldier, he probably had already been born. Azulon should have expected him to inherit, not Ozai and Ursa's children.
It could have simply been a fear of usurpation. We know how paranoid the Fire Lords were, and it's implied that the strongest firebender in the nation can become Fire Lord. If some especially prodigious heir were born to Ursa, it'd be far better if they were tied to the royal family than if they were independent, and therefore a threat.
Perhaps Azulon wanted Ursa and Ozai's daughter to marry Lu Ten, which would bring Roku's blood to the throne.
Good PR. Thanks to Azula's lie about Zuko as the one who killed Aang(and since Azula had just managed to single-handlely conquer Ba Sing Se, Ozai had no reason to not trust her), Zuko has basically become a war hero, and the idea of a banished prince returning home in such a glorious manner is a stuff of classic stories that would be too tempting to not use to silence Ozai's enemies in politics and improve even more his image in the nation. Besides, Zuko has had the chance to witness the earth kingdom first-hand which means he may had have more accurate information than any of his spies, not to mention that Zuko was basically known as the hero who efeated the avatar, which means Ozai wwas more limited at how he could deal with Zuko without raising suspicion. As far as we know, Zuko just happened to be extremely useful for Ozai at the time.
Way back in The Ember Island Players Zuko briefly comments on how his mom used to take them to the theatre where "They butchered love amongst the dragons every year". Now in the opening pages, what is Ursa's opening line right after giving Ikem the scare? "But I thought you were the Mighty Emperor, hero of Love Amongst Dragons!" Ursa and Ikem were originally part of the troupe and the lead pair!
It's not clear if they were part of the troupe, or if it was a simple village production.
It's confirmed now that Ursa was actually the most famous member.
And now we also know the origin of Zuko's Blue Spirit Mask.
To elaborate even further, there's a reason why Zuko chose that particular mask over the other. Zuko and Azula would reenact the final scene of Love Amongst Dragons, with Azula being the heroic Dragon Emperor and Zuko the villainous Water Spirit (which had the Blue Spirit Mask). Their respective roles represent the fortunes the siblings have in their actual lives: Azula being lucky and victorious while Zuko is the Butt Monkey forced into the role of an underdog and a villain.
The fire sages prophesied that Ozai marrying a descendant of Avatar Roku would yield a powerful bloodline for Fire Lord Azulon. In a way, it came true, and one conclude that the fire sages foresaw the birth of the one who would become the Fire Nation's salvation: Zuko.
Their prophecy also serves as a major bit of Foreshadowing. If you take it as fact, then Zuko can't possibly be Ikem's son. He's already the Fire Lord, so the prophecy would not make any sense unless he was a true descendant of Azulon.
Azulon's whole plan behind uniting Ozai and Ursa was to breed super-powerful Tykebombs. On his last day living, he had just sat through a demonstration of how Azula was a success in this regard while Zuko was a failure. The whole "punishment" angle he gave to Ozai when he ordered him to kill his firstborn son was just an excuse to rub out the failure so that the Royal Family isn't tarnished by his existence any longer.
Hey wait a sec, Zuko and Azula's firebending master was Kunyo, the same guy who challenged Toph's earthbending academy back in the Promise! So that's how he came to Yu Dao. And he was indeed a wimp.
The Mother of the Facesīs body resembles a leafless tree. Now, remember where Koh lives. He really misses his mother.
When Ozai asks why Ursa wrote a false letter naming Ikem as Zuko's father, Ursa tells Ozai that her deepest wish is that Zuko turn out to be nothing like him. Ozai responds that from that point on, he will treat Zuko as if her false letter was true, that Zuko is an unwanted bastard child; controlling him, making him feel worthless, burning his face, banishing him for three years and generally being an evil, contemptible douchebag. Ultimately, this mistreatment is what leads to Zuko Calling the Old Man Out and his Heel-Face Turn on the Day of Black Sun. So Ursa got her wish in a manner she'll regret for the rest of her life. Be Careful What You Wish For.
After being threatened into marriage then told she would never see her parents or friends again, do you really think the consummation of their marriage was completely consensual?
Konietzko and Di Martino said that Ursa and Ozai "started out okay", so it probably wasn't as bad as that.
"Okay" doesn't necessarily mean "happy" or "willing." The whole marriage was against her wishes, so any consummation would be equally non-consensual. She may have accepted it as being the way things are now, but that doesn't mean she wanted it.
"Started out okay" could mean anything; when Ozai first meets Ursa, he does seem happy to be marrying her, but he also callously states that she can never see or communicate with her family ever again not long after. We also have no idea when they had their first child into the marriage; it could have been anywhere from a few years to a few weeks before they started trying to get an heir.
How traumatized must Kiyi be right now? Her entire life has been turned upside-down, she's related to the dysfunctional Fire Nation Royal Family, her two half-siblings are emotionally disturbed (and one of them is mentally disturbed as well!), her father has kept the truth from her all these years, and the mother she's always known no longer exists. All in the course of one night. OUCH.
It's bad, but not as bad as really stated. She already liked Zuko a lot, so it won't be THAT drastic of a bombshell to gain him as a sibling, although his position (freaking Fire Lord!) may throw her for a loop for a while. Her father kept the truth from her, but there was really very little she could do with the truth up until that point with no proof and Ursa's memories of the Royal Life gone. As for "Noriko" no longer existing, that's not very true. Really the only change is her face, which while a bit of a shock, can be looked past. Ursa didn't lose any of her memories for the last 5 years so she'll still be the same woman and mother she always has been to Kiyi. So really, other than some initial emotional shock, she should be fine if a bit unnerved at first. The only issue...is her Ax-Crazy half-sister Azula still being potentially Ax-Crazy and would have very understandable reason to hate her. We can only hope Zuko is right and she regained a bit of sanity.
And at least it happened very early in Kiyi's life, so she'll be adjusted to her new reality for most of her life.