We cannot say for sure whether or not Hamlet would have killed Claudius that day if his mother had not died, but whatever Hamlet's plan was, it was discarded the instant he he discovered that Gertrude was poisoned. He had enough anger and jealousy burning in him to make him want to kill Claudius and enough chances throughout the show to do so, but he always refrains, even though he knows that if he doesn't kill Claudius, then Claudius will surely see him dead. It is only when his dear mother is poisoned by Claudius' hand that his sanity is truly broken and all his pain, anger and sorrow are released as he stabs Claudius with the poisoned sword and then downs the rest of the poisoned drink. his throat, crying: "Behold, you incestuous murderer, damned Dane, drink this potion. Is your union here? Follow mine