Apparently, Gertrude is not aware of the misdeeds of Claudius as the play unveils. However, she begins to doubt her assertions as the events unfold. Her beliefs are undermined after Hamlet kills Polonius and blames his mother for betrayal. He tells the truth to her concerning the death of his father and forces her to see her wrongdoing.
Gertrude doesn’t accept the truth and instead cries and beseeches Hamlet to stop, “O Hamlet, Speak no more!….” here, the reader can see that Gertrude is now seeing her mistakes of betraying her husband by opting to marry his murderer. Again, Laertes through his accusations of Claudius murdering Polonius and the story that unfolds between them puts Gertrude in a dilemma of whether to believe in the mother’s instinct in saving her son and her failure to accept the truth.
Gertrude shows her doubts in act iv as Ophelia is furious over the death of her father. As they sing in that act (IV.v.2880-2885), Gertrude pretends not to know the lyrics. This further shows that Gertrude couldn’t tolerate hearing the words in the song and so on.