WELL HERE’S ONE SUPER UNLIKELY THEORY I’VE LATCHED ON TO.
….My own foolish imaginings lead me to believe that Tarrlok’s mother was from a family of middling criminals who thought marrying off their beautiful, recently-come-of-age daughter to Republic City’s most powerful and vicious crime lord was a smart move in terms of social status. And once Yakone fell from power, they cut themselves off from her for more or less the same reason: which is why she had to flee the city with her husband.
She probably died when Tarrlok was fairly young, but she would sit down every morning and fix her son’s hair into the traditional Northern Water Tribe style. Maybe it was just force of habit for him after that, which came in handy later when he traveled there to remake his identity.
/stupid head-canon to be later and violently jossed.