That Princess is actually a cut above. It's so hard to find a girl who is that brave and decisive. I'd keep her.
She reminds me of Sherry Tyueli in Gate. That girl knew that being cozy with the Japanese diplomatic staffer would be key to access. Her feelings are probably totally genuine, but as a daughter of a noble house, she was educated to consider her body to be a strategic asset to her house, and marriage to be used for advantage.
This Princess gave a really clear and reasonable explanation of her decision, saying that her engagement would hold off other suitors until she could make a better choice without pressure, while Touya could be dropped relatively easily as an adventurer. It reminded me of the Vulcan woman's reasoning in "Mr. Spock Swims Upstream to Spawn" (I forget the actual episode title). But she quickly figures that Touya can stand on his own merits, and has a really nice character. She also quickly defuses conflict by stating unequivocally that co-wives or concubines would not be opposed by her. Despite her youth, her training and education makes her a strong candidate for "primary" wife, since she is able to skillfully manage the others.