a good influence on her son.

In act IV, as Ophelia goes mad and begins singing after the death of her father, Gertrude shows concerns, saying "how now, Ophelia" or "what is this all about?"

More significantly, later in the act, when Ophelia drowns, it is Gertrude who provides Laertes with the details, as if she witnessed the drowning herself or someone told her in great detail what happened. Again, she describes Ophelia in positive terms, first depicting her as a child of nature, then as like a mermaid floating on the water until her clothes, full of water, pull her under:

And, mermaid-like, a while they bore her up: Which time she chanted snatches of old tunes; As one in capable of her own distress, Or like a creature native and indued Unto that element: but long it could not be Till that her garments, heavy with their drink, Pull’d the poor wretch from her melodious lay, To muddy death

From what little we can see of the two women, both are used by Claudius against Hamlet, they had an affectionate bond, and Gertrude thought well of Ophelia. The two women are united in caring about Hamlet, in being confused and frightened by his behavior, and in being brought down by patriarchal society.

Hamlet characterizes women in a way that reflects the Catholic Church's paradigm of women.  Women are either good and pure (like the Virgin Mary) or prostitutes (like Mary Magdalene), it is a failing of his that he can't see women as anything deeper than that.

His mother, Gertrude, is a prostitute in his estimation because she chose to marry his uncle, his father's brother, something he views as incestuous, but she also (in his eyes) chose his uncle over him. 

Ophelia, his love interest starts out as good, pure, and virginal to Hamlet's mind but when she follows Gertrude's suit and chooses to follow her father's will (allowing her father to listen in on a conversation between Ophelia and Hamlet) over Hamlet's will, she too becomes a whore in his eyes.

Both characters are portrayed as child like, sheltered and trusting throughout the play as well as somewhat one dimensional (which is different than some of the other heroines in Shakespeare's work who are more fleshed out).

But digging deeper into their characters, there are differences between the two.  Gertrude, despite being a grown woman who has been Queen of Denmark and at least somewhat involved in matters of state, has stubbornly chosen to keep a childlike demeanor.  She's shallow and only interested in external pleasures and what the next novel pleasure will be.  But despite her shallow nature, she is deeply devoted to both Hamlet and Claudius. 

Ophelia on the other hand, is a much younger woman, sheltered by both her brother and her father from matters of state.  When Hamlet turns on her for acting like his mother (in his eyes), she's shattered by this.  No one had ever been so cruel to her before and to call her a whore and to tell her that he never loved her though he once claimed to is devastating to her to the point that it snaps her mind.   Ophelia is not afforded the same leniency in her frailty as Gertrude was.  Ophelia wanders, singing bawdy songs as a bitter reminder to others that her innocence is now gone.  When she can no longer handle one tragedy after another (including Hamlet's murder of her father), she chooses to take her own life, unlike Gertrude who died the way she lived, choosing to drink from a shiny new cup to enjoy the novelty, preferring to drink from the poisoned cup than listen to Hamlet's vague warning not to.

I'm not sure what you are asking, but I will compare Gertrude and Ophelia for you.  Ophelia is a naive and innocent young girl who is very obedient to her father, whom she loves dearly.  Ophelia is told by her father, in Act 1, sc. 3, to have no more involvement with Hamlet because Hamlet is just using her.  She responds, "I shall obey, my lord."  And she does obey which causes confusion in Hamlet.  In Act 3, sc. 1, when Hamlet talks to Ophelia when she tries to return the "remembrances" he gave her, he is brutal because he doesn't understand why she suddenly shut him out.  Also, the things Hamlet says to her indicate that she is innocent.  The harsh words Hamlet speaks to her again at the play in Act 3, sc. 2, may have helped lead to her insanity when her father dies at Hamlet's hand.  Gertrude is an obedient person, too.  When Claudius asks something of her, such as in Act 3, sc. 1, when he asks her to leave so that he and Polonius can hide and spy on Hamlet and Ophelia, she says, "I shall obey you."  When Hamlet asks her to keep secret from Claudius the fact that he is not insane, in Act 3, sc. 4, Gertrude complies.  At the start of Act 4, Gertrude twice tells Claudius that Hamlet's act of killing Polonius was done from Hamlet's insanity.  Gertrude isn't the innocent flower that Ophelia is, though.  When the ghost of Hamlet's father talks to Hamlet in Act 1, sc. 5, he refers to Claudius as "..that adulterate beast.." implying that Claudius and Gertrude were having an affair when the king was still alive.  Neither Ophelia nor Gertrude is portrayed in a flattering way; both are seemingly without much will power of their own. Both appear to be weak people who are little more than package adornments.

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.