The sister believes that Leslie would become the new favorite, so she fears that it'd affect her position. (Or that she'd be sacrificed to improve Leslie's powers). Because the father started including and pampering Leslie, the sister's been on edge on losing her spot as the favorite and was desperate in getting Leslie saved.
However, the father already planned on making the sister marry into the royal family for political power. Then using Leslie for physical/political power by forcing her to become a war hero. By setting the carriage on fire, he wants to instigate her into revealing her powers and thus giving him enough reason to turn her into a super soldier.