What role were women supposed to play according to this play? How does Glaspell show this using the dialogue of the men?

This is a thematic question and can be answered in a few different ways. Pay particular attention to the theme of emapthy and protection.

Theme of Female Identity

When speaking to the female characters in Trifles, Henderson and the other men make a key mistake in their assumption that the women derive their identity solely from their relationship to men, the dominant gender. For example, Henderson tells Mrs. Peters that because she is married to the sheriff, she is married to the law and therefore is a reliable follower of the law. Mrs. Peters' response is "Not--just that way," suggesting that over the course of the play, she has rediscovered a different aspect of her identity that ties more closely to her experience as a woman than to her marriage to Henry Peters. As Mrs. Haleconcludes, women "all go through the same things--it's all just a different kind of the same thing." For Mrs. Hale, Minnie Wright's murder of her husband is the ultimate rejection of her husband's imposed identity in favor of the memory of the person Minnie Foster used to be.

Patriarchal dominance

In Trifles, the men believe that they grant female identity by virtue of the women's relation to men rather than through their inherent qualities as females. Except for the absent Minnie Wright, the women have no first name and take their husband's last names, despite being the protagonists of the story instead of the named male characters. This institutionalized male superiority is so pervasive that the men feel comfortable in disparaging Mrs. Peters and Mrs. Hale's interest in "trifles," with the clear implication that the women are too flighty and small-minded to worry about important issues such as the investigation at hand. In addition, when the men observe the troublesome state of the kitchen, they immediately conclude that the woman must be at fault in her homemaking abilities because they all know John Wright as a good, dutiful man and in consequence form a unified front protecting John Wright's reputation. Because of this male solidarity, Mrs. Peters and Mrs. Hale can only aid Mrs. Wright if they ally with their own gender.

Empathy and protection

At the beginning of Trifles, Mrs. Wright is an unknown quantity whose behavior in Lewis Hale's account is puzzling and bizarre. By the conclusion of the play, however, the substance of her personality and life has been revealed through Mrs. Hale's memories and through a few small details contained on the first floor of her house, and her character becomes the subject of sympathy and finally of empathy. Because Mrs. Peters and Mrs. Hale come to realize the similarities between the murderer and themselves, they decide that Minnie Wright is worthy of their protection, which has several meanings for the women. Most obviously, they unify with her against the law, as represented by the men of the play, but they also protect her by not telling her the truth about her ruined preserves. In addition, Mrs. Hale regrets not having protected Minnie from isolation and solitude, and she resolves to atone for her inability to protect Minnie earlier by helping her now.