If you blinked just once, you would have missed everything Laina did leading up to the Duke's fall to the ground. Even King Dante had to take a few seconds to figure out what had happened in that span of time.
Laina indeed put her hand out, ready to shake the Duke's hand. But Duke Lackerwood did not want to shake her hand. He wanted to wrap his arm around her waist and escort her to the dance floor.
He did not care if she agreed to it or not. He was drunk and bold and he wanted to dance with the belle of the ball. Laina saw through his scheme the moment his hand reached out behind her back.
She was surprised that even the nobility lacked morals and respect. Laina was not about to let him get his way either. She grabbed onto his wrist with one hand and placed her right hand on his shoulder.