Can't explain Gertrude without explaining Hamlet, so I'll start there.
I had two breakthroughs in my comprehension of the play. The first occurred when I was 27 and working as a security guard at the Bank of America World Trade Center in SF. I worked graveyard shift, 11 pm to 7 am. The job was tortuous: it takes a great toll on the body not to sleep, night after night after night. But I only realized the absurdity of my situation a few months into it, when it occurred to me that I was staying awake ...all bloody night long....guarding thieves' money. At that point, I remembered how Hamlet starts, with a security guard scene ---changing of the guard -- while in the background the thieving/murderous king revels and drinks. That's when I realized Hamlet's double bind: that he must seek revenge for an act that characterizes not only Claudius' reign, but the reign of all power seekers before him (including Fortinbras and Hamlet's father (HF)).
Although Hamlet speaks of his father in devout terms, that devoutness is colored more by Hamlet's grief than by any evidence that HF was a different sort than Claudius. Polonius, Rosencrantz, Guilderstern, and Gertrude were who they were long before Claudius got the kingship, and there's nothing to suggest in the play that there was any transformation of those characters as a result of Claudius' ascension. So the notion that there's some natural order that Hamlet must restore is pretty much undermined from the beginning of the play. What Hamlet was before the play is a "scholar and gentleman" who could afford to have pretty thoughts in Wittenberg, while daddy took care of business at home. With daddy gone, Hamlet has to do something ...or to continue with business as usual. Everyone else is getting on with getting on, but Hamlet can't because he has a conscious intelligence and some feeling.
My next realization came as the result of my father's death two years ago. He died with no warning --suddenly, absolutely at the age of 83, after a long, productive, and fairly happy life. It was the first time anyone I loved died, and I was shocked to find that for the next year I too found most things flat, stale, and unprofitable, and that, for the first time in my life, I lost all interest in sex for about a year. All this was not because I thought consciously about my father, but because this grieving process had got hold of me and would not go away until it was done. Hamlet seems to be the only character that feels any grief for his father' and he not only has to deal with that grief, but with everyone else's complete absence of feeling. His grief is interpreted as self-indulgence, wrong-headedness, madness -- and the fact of grief cannot be comprehended in his world.
The other characters, with the exception of Ophelia and Horatio, cannot feel, but literally wallow in a sensual, self-satisfied sty -- scheming and self-seeking, including, most notably, Gertrude who, was best incarnated by Julie Christie in that ludicrous Mel Gibson Hamlet. Her physical beauty and acting were perfectly suited to bringing out a Gertrude as the trophy wife -- husband, immaterial. She's a beautiful, complacent woman who is perfectly happy to indulge herself and to navigate from husband to husband, provided her own station and comfort are assured.
So, Hamlet can only set things right by destroying this world, which he does at the end. The tragedy is that, try as he might, he cannot restore a natural order that never existed in the play in the first place. I guess that's what makes him the first "modern" tragic hero.
Joanna