Questionable Questing

He was chosen for the role of Jinchuuriki because of his highly likely relation (looking the same) to Yagura, after a successful ousting of Yagura. The reason they chose a close relative to transfer Isobu into is that Yagura proved capable of using the power of the three tails in spite of the flow-restrictive nature of the Adamant Tank seal used for it.

A seal designed so the only way the Jinchuuriki could use the power of Isobu was suicide bombing, to prevent undue influence or rebellion. Yagura was originally meant for that, but discovered his family's ability to synchronize with the three tails and managed to contact Isobu and use his power despite a seal that has a net chakra /consumption/ from the host.

Yukimaru doesn't care about his now dead former Kage relative at all, really. He never knew he had that relative. He's also not nearly as active in contacting Isobu rather than just siphoning his power or bringing out parts of him. After all, he can use the power without talking to a hateful and nostalgic beast, and the amount he can use (if not his control over it) positively correlates to strong emotions.

And I /am/ suggesting that Rin's fate is essentially how the three tails was generally used, except that it was normally put into loyal Kiri ninjas, with a seal that's actually entirely stable, except when opened.

Until they discovered a family of khaki haired purple eyed folks who could ignore the rules of that seal.

One was the boss, and the other works under new management that likes how it works out.