Claudius talks about Gertrude as if, now that he has married her, it would be his death if she left him. I think that one of the several reasons he killed his brother was that he was completely infatuated with Gertrude--in a really lustful and obsessive and even creepy way.

I also believe that Claudius is extremely persuasive--he's a true serpent in the garden (as his brother says of him). Just as the serpent "persuaded" Eve to eat of the fruit, Claudius "persuades" Gertrude (and the rest of the court) that marrying your dead husband's brother is just fiiiiine. (Eeewww!)

Last, I believe that Gertrude is male-dependent. She needs to have someone to will dote on her, worship her, and protect her (because it gives her power that she otherwise doesn't feel she has), and she has also has to feel that some man receives her affections or she isn't really a true woman. (Eeeewww!)

Glenn Close played her that way in the Zefferelli version (with Mel Gibson), and I though she made it work very well: first, she was "Niobe, all tears" and then she couldn't have been happier to have Claudius to lean on and to worship her. It's an "I'm so unhappy and so lonely, I need a man to make it all go away" problem.