It interesting since she has to work harder here than in the original for their trust. In this story, not only are they adult but the real Katherina has done some bad things already. The original is clearly easy mode since the casts are more trusting as children.
Remember guys, he a prince and she is a commoner. Unfortunately since equal right is not available in that time so she can't convict him. Also, maybe deep down she still think of him as a character with multiple ending.