Actually, I'm not so sure... Even the novel didn't clearly explain it but it was either the power to change the weather or the power to charm others.
But as I said, I don't really know, the novel didn't explain it clearly and as far as I know, the 2nd princess doesn't show up until the last part and even then she has little parts. She's like a minor villain.
Well, according to the novel, it was because he was led to believe that she has a powerful ability or that she has some powerful ability. The first prince, in the novel, has telekinesis which was viewed as a weak ability while Aristine hid the fact that she had an ability. In fact, had Aristine showed her ability, she might be crowned heir but then to strengthen her power, the king would put her in all sorts of life and death situation as it's the only way to strengthen or unlock a new part of their ability
Tbh, I honestly think she has the ability to charm others or so.

Im still so confused. What power does the blonde 2nd princess have again??????