So, I've been giving this a lot of thought and came to the conclusion that the creators came up with the Search Part 1's plot a long time ago. My bet is since the Blue Spirit episode or some time between Book 2 and Book 3. And here is why.
Firsly, the flashbacks we see in the comics are scattered and after the first one about Azulon and Ozai coming to take Ursa the flashbacks are not chronologically. It's like this - Ursa and Ikem with the masks, Ikem asks Ursa to marry him - Ozai comes takes Ursa and marries her.
After those events we have some other flashbacks but we don't know if they take place immediatly after the last ones. It's obviously they don't. When Ursa writes that letter it is hinted that she has been writing letters for a far amount of time since she thanks Elua for all her help.
Most of you said that Ozai should have banished both Ursa and Zuko after he found out but that isn't necessarly . See, we don't know what year it was when those things happened ( her writing the letter and stuff) it could have very well be the very year when she left after commting "vicious things* ( something like that) as Ozai said.
In my opinion that's why Ozai felt no remorse in killing his own son when Azulon demanded him. Because Zuko wasn't his son and he knew that. But Ursa , wanting to spare Zuko ,had a deal with Ozai. She would ensure Ozai the throne without having to kill Zuko. She would get banished for killing Azulon even though no one will suspect anything and take both secrets with her - killing Azulon and Zuko not being his son.
Frankly it makes sense to me that Ozai wouldn't want his people to know. He was the Firelord and much like the totalitarian leaders of our world he had to preserve his image of a great father and great husband. A familist. His people were afraid of him but respected him at the same time.
And for all of you saying she should have had to be pregnant when she left Hira'a that's not necessary either.
Even though Ozai didn't let her talk about her home or see her loved ones doesn't mean she couldn't have broke that rule and see Ikem one more time maybe to tell him that she was never to return again and that he should forget about her. Maybe.
The show has proven us that it won't stop for little things. e.g Tarrlock and Amon , Gyatso etc. Many many things that shouldn't be in a cartoon.
And as for the signs in the show.
Zuko said Ursa took him to see Love amongst the Dragons on Ember Island many times.
That line wasn't put there just for fun or anything. It serves a purpose.
Using the Blue Mask. Well ok that was to emphasise the fact that Zuko was still not sure of who he was , he was confused about his own self and he couldn't decide if what he wanted was what he needed. i.e capturing the avatar and bringing him to Ozai.
But again I am sure the creators had other motives to chose a theatre mask for that purpose even though we didn't know Ursa's story back then.
So overall my bet is between Ursa's letter and Azulon's death didn't pass much time and that might have contribuited to her banishment.
Ok. Not to self : we see that Zuko and Azula are a tad bit younger in the flashback with the letter. so my guess is that they werea about 10 or so when she left and in that flashback they were 5. I think.
we know when the letter writing flashback is bacause we see zuko as a very young child and azula probably not old enough to walk. and i believe that bryke didn't have this planned until later, maybe even at gene yang's suggestion: look at the events of the avatar and the firelord. that wouldn't have happened the way it did if the search was planned the way it was. bryke just used events from the series in the search and put a different explaination to them.
I totally forgot about Ursa taking Zuko to see "Love Amongst Dragons" every year. I think that the whole idea wasn't totally developed at the time, but they might've been leading up to it as a possible outing to continue the series. If you look closely, there are multiple subtle hints that Ursa was hiding much more than we ever expected. Very nice theory, well thought out, and you had a lot of great supporting facts :)