These are women married to men who represent the power of society, and the control of sporadic situation. Moreover, the women, as their wives, are paradoxically meant to represent the exact opposite: The co-dependence, the neediness, and the feebleness of the "weaker sex". However, we know that Susan Glaspell's purpose in "Trifles" is to expose the double standards of society in terms of the social expectations placed upon women.
Hence, Mrs. Peters and Mrs. Hale have the task of breaking free from the expectation that they are meant to remain quiet, idle, and useless through the investigation. In addition to this, they now have a responsibility to report the abuse that a fellow female has obviously suffered by the hand of her husband. However, all this becomes nullified when we see how, with their disclosure, there may be consequences: First, the victimized wife will have a "motif" to have killed her husband, no matter how well-justified it may seem. Second, she will inevitably land in jail. Third, there will be no way to secure her future.
Therefore, Mrs. Peters and Mrs. Hale are between the sword and the wall and there is no possible winners in their situation.
Yes, both of these women face the challenge of having to choose between submitting to patriarchal authority in the form of the Sherrif, or supporting their fellow female in her time of need. It is they of course who uncover the true motive for the crime in the form of the dead bird that was killed by John Wright. Their decision to hide this evidence makes it clear that they understand and sympathise the kind of hard life that Minnie Wright has suffered and the way that she too has been "strangled" by her husband, just like the bird.
The biggest dilemma both these women have to consider in this play is whether or not to report what they know to the authorities. It's true that nearly every piece of "evidence" the women find was also seen--and overlooked--by the men. At the same time, if they had explained their reasoning to the men, Minnie would no doubt have been found guilty of killing her husband. This is an internal conflict for both women, of course. Though she had no relationship with Minnie, Mrs. Peters can understand Minnie's rage and helplessness because of experiences in her own life. Mrs. Hale is a former friend of Minnie's and understands how difficult her life became; however, she is also married to the sheriff and knows she should not be withholding evidence.