
Both parents were in a relationship. Yamato's father, Mikasa married the Bidou Kumichou's daughter making him a Bidou and now a wakagashira. Mikasa's death is padded out. Yukio's dad is Yahagi, who was in a relationship till his death with Mikasa. It is padded out why Yahagi stayed loyal to the Bidou group rather than forming his own branch family, due to to his relationship with Mikasa. On the wedding day Mikasa's new wife says that she became the bride of two men, and it doesn't have seem to have been a negative arrangement as they all got what they wanted as far as society and the group would have allowed. This might suggest that in the future both Yamato and Yukio will have to get married to women and have an heir.

so maybe Yamato's dad was also an uke xD ( ̄∇ ̄")

It’s doesn’t open do u know if it’s on any other site?
https://myreadingmanga.info/katsura-komachi-ashita-sekai-ga-owarunara-eng-pura-bin/
the story of yamato's parents