...wow, this is so sad. I think that the anime (because I haven't played the games, so I don't know them enough to say) would have benefited if they focused a bit on Mukuro. We didn't get to see her at all, and this just makes her story seem full of feels. I'll probably translate this into English at some point if nobody else does.
There's a novel focus on "IF" route in first game which mukuro is the protagonist. http://untuned-strings.blogspot.com/2012/12/dangan-ronpa-if-part-1.html
I think if Mukuro had some more time in the original story she would have betrayed her sister. But that is what happens in the "What If" story od SD, is actually made from the game team then is "canon" if you see it in the right way. I like the "What If" World more.