Family. It didn't have to be a war between them... who loved Riku best, or who Riku loved best. That would only break Riku's heart to have them fight each other.
Corin put his hand over his heart and bowed deeply. "Yes, Your Majesty." Trust. It was hard. But he was going to try. For Riku's sake, if nothing else. Maybe... maybe he and the Prince could do something, just the two of them. Try to be... friends-ish, and know each other more as equals than rivals for Riku's affection.
So he took the Prince's kindness without looking at it suspiciously and went ahead, waiting for him to catch up so that they might walk there together. "What might we expect, this evening, Your Majesty?"