@K.aixin Thank you for guessing mine!
You've hit the needle right on the head for the base-level plot of the story, so I will give you a 7.5 rating ^ ^
The second prince is actually a promiscuous player who loves her, but cannot have her because he has to assume the responsibility of his late brother and protect his nation and the continent at war, so he takes her as a mistress instead.
There's more to the plot, but yeah, the main genre is the romance between the two, so I have to give it to you!