This is a great question. Kate Keller is a kind, sympathetic character who is nevertheless torn apart by what her husband has done and also by false hope of the eventual return of Larry. It is clear that this continued hope is not just because of the love she has for Larry and her desire to see him alive, but also because in her mind she has linked Larry's disappearance with her husband's guilt in knowingly manufacturing faulty engines that were responsible for the deaths of 21 soldiers. Even though Larry could not have been killed as a result of Joe Keller's treachery, Kate believes that her husband should be held accountable for his guilt as a murder. This false hope of Larry's return is only ended when Ann Deever reveals the letter that she received from Larry which reveals his plans to kill himself.
Because of this false hope to which she stubbornly clings, she prevents others from moving on and accepting the loss of Larry. Chris, her other son, is eager for her to be able to accept that Larry is not coming home as he wants to marry Larry's former sweetheart, and Chris is very aware that he will be unable to gain Kate's blessing on this union as long as she stubbornly refuses to face facts and admit that Larry is not returning.
Throughout the play, Miller seems to present Kate Keller as a character which the audience can empathise with. She is a maternal figure, but a character who is destroyed by her husband's actions and his guilt. As the rising action develops and we approach the climax, her inner turmoil is revealed in various physical symptoms. Interestingly, after Joe has killed himself, she tells her other son, Chris, to live, which is ironic as that is something she has been evidently unable to do after Larry's death.
A key quote for me that sums up her character is when she reveals her position to Chris:
Your brother's alive, darling, because if he's dead, your father killed him. Do you understand me now? As long as you live, that boy is alive. God does not let a son be killed by his father. Now you see, don't you? Now you see.
This explains her impossible situation - to accept that Larry is dead in her mind would be to accept that he was killed by his father - an unthinkable position and one that helps explain her inner anguish.