Headcanon Ursa post poisoning Azulon, with the help of the various fanficts that I have read. So, more like a brainstorming.
After the exile she spends some period being Toph’s Nanny, til she heard about Zuko’s scar and exile.
So she heads to the Northern Air Temple, and just as she's about to meet up with Zuko, she's kidnapped by bandits who take her to Ba Sing Se and sell her to Dai Lee. She then becomes a Jo Dee and spends years not remembering who she is.
In Ba Sing Se she is about to meet her children; in fact, she glimpsed them, having a memory lapse but unable to really remember them. When the White Lotus liberates the city, she is sold by the agents. Then she manages to escape and reaches the village of Song, where she and her mother take care of her. Years pass and she still doesn't remember who she is, partly because at this point she doesn't want to remember. In my opinion, this is the only possible explanation for what happens to her in canon. She is a caring, kind, loving mother. She loves her children and would never have abandoned them of her own free will. She would have waited for them and would never have wanted to erase her memories, so for me what happens in the comics is completely unfounded. But before all the misery this woman is subjected to, it's nice to imagine her going through this period with Toph.
Zuko finds her when he returns to make amends to Song.
Thanks to @elmetish who wrote her as Toph's Nanny after her exile.
https://archiveofourown.org/chapters/104977308?show_comments=true&view_full_work=false#comment_1200590141
Thanks to @Seyary_Minamoto on ao3 who wrote her as a Joo Dee, and Song is helping her to recover.
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Then for my Zutara headcanon, a couple of months later, Zuko and Katara talk about their mothers again, and Zuko tells her that he actually suspects she is alive.
Then they change the subject, Katara talking about the Joo Dee. She's been there recently, in Ba Sing See, with Aang and Toph on her travels through the colonies. They were headed to King Kuei. She says they were all people with pasts, some daughters, some mothers, and she feels great pity for them. She tried to heal some of them. Suddenly, she says referring to her past experience, “I met this woman in Ba Sing See. She had golden eyes.”
Zuko says there could be definitely women from the colonies. He tries not to get his hopes up, dismissing the possibility, since all his attempts to find her have yielded no results. And they drop the subject. Even though Katara tells him she'd definitely help him with his quest, to give him closure as he did for her.
Then she tells Zuko to take a vacation from his duties as Fire Lord. So Zuko spends this vacation visiting the villages wanting to make amends with. Without directly looking for his Mother, he finds her in Song’s village.
