From a practical standpoint, it does seem like marrying the prince is the best option for her. She has lousy alternatives and the spinster/lesbian route won't be publicly accepted, she'll get a not-insignificant amount of political leverage with the position, and she'll even get to support her new bestie's love to boot.
That last part strikes me as significant in particular because kids don't have to grow up with the same ideology as their parents. By assisting her in the one point of individuality that caused the most separation from the rival faction, she can essentially strip them of their leading family within a generation, which should make the kingdom more stable.