That's all you really need to know about why Kakashi's hand is through Rin. Here's the likely scenario:

The zetsu told Obito that Rin and Kakashi were in a situation facing multiple jonin. I don't doubt it. The two are fighting them off, and, suddenly, Kakashi's sight is blinded by an unknown jutsu. All he sees is blackness. He hears Rin and is fighting blinded to protect her. He lights up his chidori and stabs in the direction of one.

The jonin all sink into the earth and disappear, releasing the jutsu. As the jutsu releases, both Obito and Kakashi's vision become clear; Kakashi has just killed Rin. Obito shows up just in time, all according to Madara's plan.

As Madara predicted, Obito will return to Madara thanks to this staged event.