Is there proof that Hamlet does not kill Claudius because for the sake of his Mother?
Hamlet had chances to kill Claudius, such as when Claudius was praying. However he didn’t kill him then because if he did, he believed that Claudius would go straight to heaven. Also as for hesitating because of love for his mother, I don’t think so. When he kills Polonius in his mother’s room, he actually thought it was Claudius. He didn’t hesitate, and didn’t think of his mother at all. For the second part, can Claudius really be considered a good king if he killed his brother in order to get the crown? He also plotted to kill Hamlet by sending him to be kidnapped by pirates.