I guess madara/Izuna killed her in the war, Zetsu maybe was showing obito her death, and that kakashi could not save her. But nobody really knew who it really was, even not obito so that may be a reason why he got raged. Afterwards Madara or Izuna went to him and explained him everthing about war, and that everthing what this generations leave to the next ones is hatred. So maybe Izuna/Madara as one of the most important Uchiha in history of Konoha trained him, they me told him everthing about konohas real face, and that even the other uchiha just became meaningless...well Obito was really pride of beeing a uchiha, and hearing that made him believe that there is nothing left for him anymore then hatred, so this world has to sleep united with him, where he can live a life he disired.
Maybe Nagato was there to bring Rin back afterwards they got the yuubi and moon eye plan done, so he could live with her. Just a guess~