Hamlet's relationship to his mother, Gertrude, is a love hate relationship. We see very little direct evidence of this love, but his extreme disappointment of her hasty marriage to Claudius implies that he once held her in high esteem.
By the end of the play, it becomes clear that Gertrude had nothing to do with the plot to kill the king. However, she did marry Claudius less than two months after the king's death, so Hamlet's disapproval is somewhat justified. Over the course of the play, Hamlet can not get over this hasty marriage, and his disgust with his mother's actions become his perception of women in general. In fact, his mistreatment of Ophelia is as much a result of his revenge plan as it is a result of his frustration of women in general. And this has to do with his disapproval of his mother's actions. His mother becomes the model for all women. As soon as Hamlet's perception of his mother is degraded, so is his perception of all women.
From Gertrude's perspective, it is difficult to say if she has any shame for remarrying so quickly. She is generally concerned with Hamlet's happiness. So, on one hand, she is an innocent and benevolent player but that innocence may also be a product of her obliviousness. She doesn't know her son very well; if she did, she may have been able to see through his “madness” and figure things out.
In Act 3, Scene 4, Hamlet really lets Gertrude know what he thinks about her and the marriage to Claudius.
Such an act
That blurs the grace and blush of modesty;
Calls virtue hypocrite; takes off the rose
From the fair forehead of an innocent love,
And sets a blister there; makes marriage vows
As false as dicers' oaths—(III.iii.45-50).
The deterioration of Hamlet's relationship with his mother has everything to do with Claudius killing the king. However, Hamlet allows his assumptions about his mother's alleged thoughtlessness to defeat any secondary thoughts about the possibility that she is just easily manipulated by Claudius. And Gertrude's obliviousness and dependency on Claudius initially screen her from seeing Hamlet's perspective on all this and/or Claudius' guilt. Some critics have concluded that Gertrude is more perceptive than previously thought. However, even if this is the case, she does little with any of these alleged insights.