In season 2, how did Koichi manage to obtain Aoi Tsunemori's ear?
What really happened, based on the evidence in the anime was:


[Intro] Togane really wanted to color Akane's Psycho-Pass black.
Togane told Mika to find where Akane's grandmother (Aoi) lived. The plan was to make Akane's playing role as Kamui's killer (by assuming that Kamui did something bad to Aoi, and Akane would take a revenge)
Togane knew that Koichi had a connection with Kamui when Yayoi were doing the investigation.
Koichi received a call, and after the call, he told Kamui that he had a doubt about the intel (possibly Togane), but they got their trump card (possibly Aoi's ear). However, Kamui didn't approve Koichi's plan since he believed that Akane's Psycho-Pass wouldn't be affected anyway. Koichi responded it as a test to Akane.
Akane and her team came, Koichi shown "the vision of hell" to them, and lastly before he gave in, he gave a present to Akane.
[Outro] Togane killed Aoi inside the car where she was held as hostage.


Actually, it wasn't clear who cut Aoi's ear. There are 3 possibilities: 


Kamui knew the location in the first place and told Koichi.
After Mika found Aoi's location, Togane came, cut her ear, captured her and gave the ear to Koichi.
After Mika found Aoi's location, Togane told Koichi her location, and he did it instead of Togane.


The first one is impossible, based from Kamui's reaction to Koichi's plan. Second one is the most believable, judging from Togane's act &amp; expression. But the third could be the the truth, based on Aoi's last word to Togane, "Are you one of Akane's colleague?", implying that she never encountered Togane before, and how the cut was taken care off, something that Togane could never do it (he killed anything).