Aisare Isekai Hanayome wa, Kindan no Koi ni Mi wo Kogasu.

Reincarnated into a world of dual monarchies, former teacher Mito is destined to become a princess. But the school for brides-to-be becomes a gilded cage when she catches the eye of the wrong man: the Black Prince Dian. Their connection is undeniable, even as they both have their own brides-to-be. As their secret trysts intensify, the White Prince, Heal, grows suspicious-and his obsession takes a coercive turn. Caught between two powerful rulers and a destiny she never asked for, which king will Mito choose to serve? (Source: MangaPlaza)