Yukiji was a very beautiful and elegant woman who lived 500 years prior to the start of the story. She was usually very guarded, composed and blunt, showing kindness only to those she deemed trustworthy. Having been taken into her current family after her entire village was destroyed by youkai, Yukiji carried a deep hatred for them. Her biggest wish was to make a family of her own, so she didn't have to be alone anymore.
Her relation to Tomoe:
Tomoe had fallen in love with Yukiji after she rescued and hid him from a mob, and went so far as to make a contract with a fallen god in order to become a human and spend his life with her. However, Yukiji ended up marrying and having a child with another man, and the contract turned into a powerful curse that threatened Tomoe's life.
While traveling back in time in an attempt to cure Tomoe's curse, Nanami discovers that it was actually herself who saved Tomoe and nursed him back to health, not Yukiji. While Yukiji did express gratitude towards Tomoe for saving her from Akura-Ou and helping her with the pregnancy, she was never actually his lover, and the one Tomoe had fallen in love with was Nanami.
Her relation to Nanami:
She is Nanami's ancestor and was given the Water Dragon's eye to help her carry along the pregnancy that would've cost both her and the baby their lives otherwise. The eye is passed on through her descendants (all of whom were female), ensuring good health until the birth of the next generation and eventually ending up in Nanami's body. For this reason, Nanami comments that she feels peaceful whenever she hugs Yukiji, even if she doesn't know about their relation.