I'll be honest, this was the worst chapter so far. I really respected her attitude of standing up for herself and using people she had every reason to fear, so to see her freeze up because some minor noble was a shit was disappointing. She could easily have him seized by guards and kicked out without anyone batting an eyebrow, being nice to him seems like a very stupid play. What on earth could he do with the support of the Emperor, Prince, and Duke all behind her?
Edit: I should also mention that having the Duke come in and save her rather than having her face it herself is irksome. This is something she has to get over herself, not have a knight in shining armour deal with every time.