It is the job of the DM to let your characters use their skills and abilities to affect the world around them. It's a pretty easy check to fail, even if you are specced for diplomacy, let alone if you are playing anything other than a Warlock. A rogue or a fighter is basically doomed to fail the check with no other alternative. A wizard with charm person *might* think to use the spell before the interaction, but that's unlikely for most people.
Karga is not supposed to be an evil character, but her introduction is to kill a scared child in front of you, then act sanctimonious about it after the fact. That's just bad story telling.
Sorry, no. You dont get to dump Cha then complain about failing social interactions. Having the kid dies forms the narrative just as much as having her live. Try playing it both ways and see how the story progresses, its interesting. You don't always get to win. You DO have a chance. You just failed at it.
