The are obviously many answers to your question, but I can only give my own opinions. Were I a scholar or Shakespeare enthusiast I could point you to dozens of different critics’ works about Gertrude.
But here are my two cents. Essentially I think you about right in that she is somewhat clueless and self-absorbed. I don’t however believe that she is a co-conspirator with Claudius. Why? Because the King’s ghost doesn’t seem to blame her for his murder and even warns Hamlet not to kill her when they are in the bedroom together. She isn’t a target of the dead king’s revenge. Nor does Hamlet, when he is listing out her many crimes, include her as a conspirator in his father’s death. Her sin is “hasty remarriage,” which Hamlet in his manic state inflates to be “incestuous and filthy”. My interpretation here is that Hamlet is being too hard on his mother. She after all doesn’t know that Claudius is guilty of fratricide, doesn’t know that Hamlet has been charged to avenge the murder. I can forgive Hamlet for this though, since Gertrude seems kinda thick about the whole situation and needs to be bluntly called out to understand why Hamlet is so upset. In other words I think the Queen is insensitive and shallow, and she can be blamed for that, but I think Hamlet unfairly puts too much blame on her. She doesn’t have anything to do with the murder, but she does remarry too quickly, allowing herself to be a pawn in Claudius’s power play, giving that much more validation to Claudius’s new status.
A lot of directors and critics see an oedipal undertone to Hamlet and Gertrude’s relationship, so much so that it has become somewhat standard to up-play this in productions these days. Personally I think it’s a stupid and unnecessary addition to the play that was never intended by Shakespeare, an interpretation driven by a silly modern obsession with Freudian motivations or by a misunderstanding of the use of the word incest in the play. To me it muddies the core meaning of the play by adding an unintended and contradictory element to Hamlet’s motivations and dilemmas. The play is about Hamlet, a scholar, a thinking man, a theologian, a gentleman, an intellectual, a contemplator who is suddenly charged to become a completely different person, to take on role antithetical to everything he is. He is asked to become a man of action, a killer, a man willing to commit murder. He is asked to set aside his contemplations, his theological considerations, his gentle nature, his intellect and become the great avenger. He handles this charge rather poorly, as most of us would handle being charged with taking on a role completely opposite to how we currently live. Adding in this bit about his wanting to shag his mum turns Hamlet from a good man doing a bad job in trying to take on a new role in life, into a plain basket case being swept around by competing emotions in his head. Knowing how Shakespeare sets up his dramas I can say confidently that the former is far more likely to have been his intention than the latter.