Princess Ursa left the capital years earlier as part of a deal with
Prince Ozai, wherein she poisoned Fire Lord Azulon, allowing Ozai to become Fire Lord.
As revealed in the backstory in the follow-up comic The Search, she was very unhappy with the arranged marriage, and made that deal in order to escape back to her home village. Additionally, Azulon was planning
to kill Zuko to punish Ozai for seeking advancement when Prince Iroh's only son died
and Ozai believed
Zuko to not actually be his genetic son,
all of which was washed away by Princess Ursa taking that deal.