I LOVE this question! Just like Hamlet himself, we the audience are too busy "thinking" about the main character of this play! We always think of Hamlet with his tragic inaction (or perhaps his tragic trust of the ghost or his madness), but we never seem to consider that Gertrude is the woman who married the murderer of her own husband! We are never told if she "knows" of this murder, or if she is simply burdened with a marriage to her husband's brother so soon after the strange death of her husband. Let's look at Gertrude's different loyalties in turn (to Hamlet's Father, to Claudius, and to Hamlet himself), and then relate how she is conflicted.
Loyalty Towards Gertrude's Late Husband, Hamlet's Father
Even Claudius hints at this when he says "with a defeated joy, / With an auspicious and a dropping eye, / With mirth in funeral, and with dirge in marriage" does he marry Gertrude. To say anything else would be inappropriate. Does Gertrude instruct him as such? We don't know. But we do know that even in instructing Hamlet how to act, Gertrude does call Hamlet's dad "thy noble father." This is truth and definite loyalty to her late husband.
Loyalty Towards Gertrude's NEW Husband, Claudius
We can see this loyalty in her simple act of marrying Claudius. This, of course, is not just a marriage, but marriage in a very short time after the death of her husband. If she didn't do this out of loyalty to Claudius, no matter how she felt about him, good God, WHY would she have done it! She expresses this loyalty (to Hamlet's disgust) here:
Good Hamlet, cast thy nighted color off, / And let thine eye look like a friend on Denmark. / Do not forever with thy vailed lids / Seek for thy noble father in the dust. / Though know'st 'tis common; that all lives must die, / Passing through nature to eternity.
In other words, if we can read between the lines, Gertrude is asking Hamlet to please stop looking so glum and downcast so near to her wedding!
We can also see Gertrude's loyalty to Claudius during the "play within a play" when she first is bothered by the Queen character. ("The lady doth protest too much, methinks.") We can infer here that she wants nothing to do with a comparison between herself and this queen because of what comes next: the murder of the king, and the marriage to the king's brother! When this happens, Gertrude does exit quickly with Claudius. We do not know whether she is surprised at his reaction (of standing and fleeing) or what, but we DO know that she accompanies him: a sign of loyalty.
Loyalty Towards Gertrude's Son, Hamlet
Even from the beginning, although Hamlet does not take her advice and "cast his nighted color off," Gertrude does beg Hamlet, her son, to stay with her when she says, "Let not thy mother lose her prayers, Hamlet. / I pray thee stay with us, go not to Wittenberg." And, remember, Hamlet often rails to US, the audience, not in front of Gertrude. The few barbs he throws at her are daggers in her heart.
My next idea would probably make a few scholars squirm, but I really think that Gertrude allows Rosencrantz and Guildenstern to talk to (spy on?) Hamlet because she LOVES Hamlet and wants to know what's wrong with him.
Good gentlemen, he hath much talked of you, / And sure I am, two men there is not living / To whom he more adheres / ... / I beseech you instantly to visit / My too much changed son.
Further she replies "amen" to their promise to be "helpful to him" right before she okays Polonius to observe Hamlet as well. Gertrude WANTS Hamlet to be happy. She cares about his love interest, Ophelia. She hopes that her "good beauties be the happy cause / Of Hamlet's wildness." Gertrude, in her despair, does attend Ophelia's funeral and is also the one who cries "sweets to the sweet."
Even though there is a question as to incestuous feelings of "loyalty" towards Hamlet, especially the famous bedroom scene, what is more important in that scene (besides the killing of Polonius) is that we hear admission of the Queen's innocence when she says, "As kill a king?" (Unless, of course, she is lying.) It is during this scene that Hamlet lays it all out for Gertrude and, if she wasn't already conflicted, she sure is now!
Thou turn'st mine eyes into my very soul, / ... / These words like daggers enter in my ears. / No more, sweet Hamlet.
And then, when Hamlet sees the ghost, but Gertrude does not (or at least says she doesn't) she says her most conflicted words of the play:
O Hamlet, thou has cleft my heart in twain.
Gertrude has her final loyalty to Hamlet right before she dies. Claudius, of course, has poisoned the cup for Hamlet to drink. We truly don't know if Gertrude knows it is poisoned or not, and it can be played either way. But I think of her drinking out of that cup as suicide. Claudius implores her, "Gertrude, do not drink." Gertrude's exact words are, "I will, my lord; I pray you pardon me. / ... / Come, let me wipe thy face, [Hamlet]." Her last gesture of love towards her son? I think so. And in doing this, she proves her ultimate loyalty to Hamlet in killing herself instead of living with regret. Claudius, of course, is then killed by the same poison.
In short, as you can see, it is Gertrude's loyalty to Hamlet that causes Gertrude to be the most conflicted. In this Educator's opinion, Gertrude redeems herself through her suicide as a last expression of love to her son. And isn't suicide the ultimate act of someone with conflicted loyalties? Gertrude is so very conflicted that she may have been driven to suicide through the poisoned pearl in the cup a the famous duel in the end of the play, ... the one where everyone is dead upon the stage (except Horatio). Gertrude wants everything to work out okay. In reality, I think Gertrude hates conflict above all. When it "working it out" is an impossibility, Gertrude ends her life.