Well, it all comes down to the fact that even her "evil side" (hereafter referred to as "Anna") still has morals: heavily influenced by the way she died. Notably, she died watching her family be murdered, so she still does her best to protect the rest of her surviving family. Also, as a bit of a quirk, watching innocents be put in a position similar to how she died really, really angers her.
"Good side" (hereafter referred to as "Mana") would probably end up reconnecting with Anna's surviving family, (and I can imagine both sides agreeing to show up to her surviving cousin's birthday parties), and technically pings as a sister for Anna's "Family Protection" mentality. Just a whiny, goody-goody younger sister.
End of the day, they're both the same, except they have different methods, drives, and mentalities. It's just that Anna is an extremely violent person, and Mana isn't.
:Edit: Apparently, Cassandra Cain, ends up becoming the second Batgirl. That's hilarious, I had no clue that was in the canon.