Ursa was banished, though we never find out where she went. In the series itself we never know if Zuko and Ursa are reunited but during the San Diego Comic-con, it was announced that Zuko and Ursa's reunion had been made into a storyboard then dropped by was a request by show co-creator Michael Dante DiMartino.
No not yet i heard rumors that they made a book 4 but it got banned and another rumor about book 5 but i doubt it. Zuko asked Ozai when Ozai was in prison at the end of book 3 and in the episode of The Day of Black Sun part 2 the invasion Ozai explains everything she was banished and is alive
Here's what really happen:
She had over-heard Firelord Azulan sayin he would have to kill zuko but she swore to protect him and firelod azulan thought Ursa was disputting her word so istead he banished her and put her in ba sing se.
well my guess would be that zuko probably did go looking for his mom ..... but the way the AVATAR team showed it is like their goanna make a sequel to it ... somethin like AVATAR 2.....cause for almost all the characters they showed a small glimpse of their history and then later on they keep elaborating it ... Jus imagine if this really does happen .... it's gonna be great.
anyway indian NICKELODEAN channel sucks big time ... AVATAR comes like 3:30 in d mornin ... and its still stuck with book 2 'EARTH' .... after this its all again with "the boy in the ice berg" i saw the entire stuff via torrent. God bless the person who came up with this ..... or else man i would have been lost !!!!!
Zuko's mom found out when Azula was in Zuko's room and he's muttering Dad would never do that to me. So she traded places with him and got banished, he doesn't find her in the series. It tells us in The Day of Black Sun, when Zuko told Ozai the truth.
She did not die, she was banished, or else why would Zuzu want to find her in the Search? All will be revealed in the Search, release date is March 20, 2013. Now what I'm saying is I hate their mother.
The answer can be found in the graphic novel "The Search", of which parts 1 & 2 are available now, with part 3 being released in November. If you'd like to experience it yourself, I'd advise you stop reading now as there will be some spoilers.
Now, what happened to Zuko's mother is that she found out from Azula that Ozai was ordered by his father to kill his own son as punishment for his insensitivity towards his nephew's death. To convince Ozai not to, she offered to make for him an undetectable & untraceable poison that he could use to kill his father & take his brother's rightful place on the throne. He accepted on the condition that she go into exile to ensure that he himself doesn't suffer the same fate. Though she wanted to take her children with her, he refused as they were his insurance that she would keep her word.
As for whether or not Zuko found her, that question has yet to be answered in the final part of "The Search". However, based on what was hinted in parts 1 & 2, I do believe that Zuko & his companions (Aang, Kitara, Sokka & Azula.....yes, I said Azula) had already came across Ursa during their search; they just hadn't recognized each other as Zuko & his comanions were in disguise in order to "avoid being mobbed", while Ursa's children didn't recognize her due to the fact that she & her boyfriend (now husband) Ikem had their appearances changed by a Spirit known as the Mother of faces & taken new identities as well (this last part is pure speculation, but the hints shown thus far point strongly in that direction.)