We know Yagura was being controlled by long-haired Tobi, but how?
That's a great question. Not only was Yagura a jinchuuriki, but he was supposed to be one of the few perfect jinchuuriki with a perfect bond with his Bijuu. In theory, those kinds of jinchuuriki should be immune to genjutsu.
For Tobi (Obito) to have controlled him anyway, with complete control for over a decade or more, is pretty impressive. That seems like a more powerful genjutsu than either Itachi or Shisui had (and those were both better with genjutsu than Sasuke has ever been).
And if his occular genjutsu is so powerful, why didn't he use it on Minato and end the fight immediately? Or use it on Konan immediately and save himself an eye (and an arm)? Or use it on Danzo at some point in order to steal Shisui's eye? If Obito/Tobi has such a powerful genjutsu, he could have used it in a lot of useful ways, but he didn't.
In fact, why use Akatsuki to capture Jinchuuriki at all? If he can gain perfect control over them, why wouldn't he go out and control all the jinchuuriki directly, and force them to come back to akatsuki headquarters without a fight?
And if he was in complete control over Yagura for so long, why didn't he capture the 3-tails during this time? Why was the 3-tails able to roam free after this point?
There are a lot of things that really don't make sense here.