So it is safe to assume Obito got his by seeing Rin die. But how did Kakashi get his? I was thinking maybe since it was not his eye he could never be the one to awaken it. Maybe since he saw the closest person to the owner of the eye die, he would be able to activate the Mangekyo Sharingan, but being a non Uchiha it would take him a long time to discover he had these abilities. Which might explain why he didn't have it until Part 2.

That or Kakashi never had any reason to use it in part 1. But I think he said he wanted to try a new technique when Naruto and himself were chasing after him to get Gaara's corpse back. Not 100% sure, just a thought.