I think the second prince is ok and cares for the fl.

+Spoiler+
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Yuuuup! He actually cares for the fl. There was a scene where he killed the 5th (not sure) prince in front of fl and the reason why the 2nd prince did that is because the other prince is trying to kill fl. He is actually cares for the fl and is ready to give his life for her. Also, I read that aside from having the same father he and the fl have the same mother. Not sure if its accurate though.