Misumi, former kumichou of the Shinsekai appointed Hirata who was wakagashira to inherit his position, on the condition that Hirata made Yashiro his wakagashira. Hirata has had a low opinion of Yashiro from the start, as has already been discussed at length in the comments. Misumu is now member of the head group the Doushinkai, and is acting as chairman whilst the Kaichou is in hospital. The group thinks the Kaichou will step down and Misumi due to inherit this position. Misumi wants to use his influence to promote Yashiro into being his deputy at the Doushinkai. So this would be a bigger promotion than just being made Kumichou of the sub-group, he would be Hirata's superior now. Hirata has been colluding with the Gouda group over drug trafficking, as the member of the Gouda was aiming to be promoted to the Sanwaikai group, meaning Hirata thought he could defect. Trafficking and dealing drugs has a zero tolerance policy within the Doushinkai group, likely due to it not being something the police can easily overlook and there are other means for their group to make money. Anyway, Hirata manages to get Ryuuzaki to be involved in the drug deal due to pressuring him about his feelings towards Yashiro. In terms of status, Ryuuzaki is Ryuzaki-kumicho of the matsubara, but he's still lower in the food chain than both Hirata and Yashiro due to his groups position. Ryuuzaki then is ordered to send a bullet out to kill Yashiro, but doesn't want this, so makes the bullet not shoot to kill. Yashiro was colluding with the police in order to get information about what was going on in relation to the drugs. He eventually understands that Hirata is the culprit. He manages to use this collusion to frame Ryuuzaki by planking the drugs at his office, this saves Ryuuzaki from being killed by Hirata. Ryuuzaki was still stabbed by Hirata, and is in intensive care. He's in police custody, and the Doushinkai group have dissolved the Matsubara meaning Ryuuzaki has been expelled. So, the drug deal with the Gouda group has been a failure and the Gouda still want a return on their investment. Hirata ends up sending someone to murder the Gouda group, then he sends out someone to shoot his own groups office, injuring Sugimoto. He likely expected Yashiro to be there, but he was at the clinic, so he sends out someone to shoot him there but this fails. This has been the fourth time Hirata has tried to get someone to shoot Yashiro, who is technically his "son" within the yakuza family. So Yashiro survives thanks to Doumeki. Amou and Misumi are aware of everything, Amou is friends with one of the Sanwakai members and tells him about Hirata and the Gouda's plans to become part of his group, to which he isn't that pleased about. He says that the Gouda man is more motivated by obtaining Hirata's profits more than anything. He then says why can't the Doushinkai just expel Hirata, but Amou says things are a bit tricky due to the group now being involved over a battle for succession. The Sanwakai man ends by saying that Hirata's behaviour has made him as good as dead. Hirata then tries to put the blame on his drug deal solely on Ryuuzaki and Yashiro, painting Yashiro as the architect. He also tries to frame Yashiro for the Gouda murders, by colluding with Inami from organised crime (who already is bitter about Yash and Doumeki). It's improbable that Yashiro, who is still nursing an unhealed wound from being shot would be running away and involved, but the top group feel that Misumi is showing favouritism towards his former "son". Yashiro tried to then deal with Hirata by himself, he abandoned his subordinates and tried to leave Misumi. Doumeki intervened, meaning Yashiro had to send Hirata's former 'cleaner", Amaguri (or chestnut as he's known) to go meet with Hirata.
So that's where we are at. We don't know how far Amou & Misumi will go in order to deal with Hirata, seeing as they know the truth. We don't know if the Doushinkai will support Misumi becoming Kaicho, or if they will try to expel Yashiro. We don't know if Inami will manage to take Yashiro into custody and frame him for Hirata's misdeeds. We don't know what Yashiro was planning when he called up Amaguri.
Anyway, that was just a quick summary from the top of my head, so likely hasn't been that helpful. :)
All the Yakuza politics have completely confused me. I'm just reading this for the romance. Even though they keep FUCKING IT UP. But it's okay. I'll live.