Responses
The Duke himself admits to his barging in as a hasty movement that led to their house being caught in the trap. Also, the court is not believing the 7yo per se, they're believing the one who is backing that 7yo who is the imperial first prince—the most likely candidate as the crown prince. The imperial power has been shown as a force to reckoned with in this manhwa, and that's why even though it is absurd to believe the testimony of a 7yo, if it's a testimony backed by the first prince, the court will wholeheartedly accept it.
Last few chapters were annoying and fast paced. Duke barged into that guy's place with no physical evidence, the court believed a child's unsupported claims even though her family is literally criminals, and a 7yo child suddenly remembering a simple conversation that happened years ago? Slim chances.