Throughout Hamlet, Gertrude comes across as a poised, kind woman who loves her son and loves Ophelia as her hoped-for daughter-in-law. Gertrude is especially concerned about the erratic behavior of Hamlet, whom she fears is reacting badly to her "o'erhasty marriage" with Claudius, as well as to his father's death.
Gertrude's relationship with her son is one of a concerned mother worried about his erratic behavior. She also wants to smooth the cracks in the relationship between Claudius and Hamlet. She is willing to engage in subterfuge to try to get information about what is really going on in her son's mind.
When, in a frenzy, Hamlet accuses her of having traded a husband like a "Hyperion" or sun god for a much lesser man and asks how she can have lowered herself to share a bed with Claudius, this picture of her own corruption in marrying for convenience's sake stabs her through the heart. She cries out:
O Hamlet, speak no more!
Thou turn'st mine eyes into my very soul,
And there I see such black and grained spots
As will not leave their tinct. (3.4.89–92)
Her ability to see her faults and express anguish over them shows she still has a conscience.
Her tenderness towards Ophelia comes out at the funeral, in which she says she had hoped Ophelia and Hamlet would wed:
I hop'd thou shouldst have been my Hamlet's wife
I thought thy bride-bed to have deck'd, sweet maid,
And not have strew'd thy grave. (5.1.220–222)
Ophelia is an innocent young woman who is confused by Hamlet's behavior. She wants to think of herself as his girlfriend, but she has been warned by her brother and father that she must be very careful in dealing with a prince, who might use her and discard her. She is an obedient daughter and tries to pay attention to her father's advice. As for her relationship with Hamlet, she is hurt at his cruel humor, such as his telling her repeatedly to go to a nunnery, a word which puns on whorehouse. She believes he is mad when he says this and cries out:
O heavenly powers, restore him! (3.1.153)
She also can't understand why he has murdered her father, and her distress eventually leads her to madness and suicide.