HMM. Part of me thinks it would be funny to make her Izanagi's cousin because they would probably get along well enough until she realized who he was. But idk. She could also be Ryujin's cousin - depending on how close they were and how comfortable he'd be with it, she would've totally loved visiting his kids and being like a cool distant-auntie or somesuch.
fff Izanami would like to remind him that he's the one who came for her and either COULDN'T LISTEN TO DIRECTIONS LIKE HE WAS SUPPOSED TO or WAS THE ASS WHO REJECTED HER. or some combination thereof, really.