She wasn't being a 'brat' she Lost her mind. wewe think Zuko was the only one badly affected kwa the family drama? She had nobody but Ozai- who corrupted her into being a weapon. She had no love. She's also only 14.
Zuko had her committed to a mental institution, and in the hivi karibuni graphic novels "the Promise" and now "the search-part 1" Zuko saw to it that she was well cared for. In fact, in "the tafuta part 1, Zuko has her released from the institution to jiunge him in searching for THEIR mother. Unfortunately we see her still behaving "badly" and having delusional conversations with Ursa.