Kyoko Kuroda was the wife of Ryuichiro Kuroda, mother to Yuriko, and grandmother to Kumiko. She is mention few times in the manga. And a young version of herself is cameo when her future husband was training to be in the Yakuza
Very little is known about Kyoko other than Ryuichiro's marriage to her helped him climb ranks to be a Yakuza boss. But there was love between the two. Its also noted that Ryuichiro remained a bachelor for many years since his wife's passing.
Their marriage and lifestyle had a deep affect on their daughter Yuriko over the years. While Kyoko had adjusted as the wife of a mob boss, her daughter didn't want to have that life. She saw how many worried nights her mother had after Ryuichiro returned from fights. So when time came that Yuriko found love, to her shock she found herself falling for a man in the Yakuza like her mother had.
So to avoid that life she ultimately left her father and the family to find a quiet life.