It feels like a pretty big contradiction that she's insulted by everyone all the time over her powerlessness, but also has a reputation of being an ice demon full of wrath who will bring down her anger upon you at the slightest thing. If she had a hair trigger, it wouldn't be possible for people to keep up their abuse of her as a normal thing. And people who are constantly put down and abused don't tend to have huge egos.
Edit: Little sister's treatment of her also seems weirdly two-faced. Does she care or not? If she's only pretending to care, why do so in front of a guy who already hates the mc?