One thing is certain: Hamlet is convinced that Gertrude has some complicity in the death of his father. For, in Act I, after having spoken with the ghost of his father, in a diatribe Hamlet calls his mother, "O most pernicious woman!" (1.5.105). When he visits her in Act III and speaks with her, Gertrude does perceive her shame in having so quickly married Claudius,
O Hamlet, speak no more!Thou turn'st my eyes into my very soul,And there I see such black and grained spotsAs will not leave their tinct (3.4.90-93)
However, when Hamlet accuses Claudius of being "A murderer and a villain" (3.4.98), Gertrude begs Hamlet, "No more" and thinks he is "mad." At this point, King Hamlet's ghost enters and implores his son to be kind to his mother. In this "closet scene," Gertrude does admit to her sin of lust in marrying Claudius, but she does not seem to realize what her new husband has done.
In Act V, Scene 2, there is some suspicion created in the reader that Gertrude may realize that Claudius's intentions are evil in arranging the duel between Laertes and Hamlet. When Claudius tells her "Our son shall win" (5.2.263), she notices instead that Hamlet is winded and out of shape for such a duel. Offering Hamlet her "napkin" with which to wipe his brow, Gertrude encourages him, "The queen carouses to thy fortune, Hamlet" (5.2.265) in opposition to what she believes Claudius feels. Then she picks up a goblet to drink, and Claudius shouts, "Gertrude do not drink" (25.2.267), but she replies, "I will, my lord; I pray you pardon me" (5.2.268).
It is at this point that Gertrude appears to realize that Claudius has plotted the death of her king, just as he has plotted the death of her son. But, this time Gertrude intends to prevent death...
to Denmark's royalty by sacrificing herself in place of her son, a sacrifice she would quietly make until Laertes is struck with his own sword and cries out. Then, when Hamlet sees Gertrude and inquires how the queen is, the false Claudius says she is fainting over the sight of Laertes's and Hamlet's blood. The falseness of Claudius proves his treachery and his culpability for the murder of King Hamlet; this, then, forces Gertrude to warn Hamlet, "The drink! the drink! I am poisoned" (5.2.289) and she dies, hoping she has saved Hamlet and redeemed herself in her son's eyes.