Laura may be considered a difficult character for two reasons. The first is that she is young and impressionable and doesn't yet have her own mind fully under her own control. The second is that the exact nature of her epiphany and character change at the end of the story is open to examination because she never clearly states her final idea beyond "isn't life--?" although there are some very distinct clues to what she is thinking and experiencing.
Since Laura is young as described above, she has neither the strength of her moral convictions nor the power to enforce her moral convictions. So, while she has a good moral impulse when she hears of the death down the lane, she can't hold to it in the face of a black hat with velvet ribbons nor can she exert her moral convictions over the rest of the household and actually impose what her convictions tell her to be a correct response. This brings up another point related to her youth. Laura doesn't have an idea of what is appropriate and possible and what isn't, in addition to which, she isn't calloused by previous encounters with death: this is her first encounter.
The ending of the story narrates Laura's experience with the dead carter apart from any previous personal or emotional ties to him, so Laura can see his death as purely a metaphysical or spiritual experience, whereas his widow feels his death as a physical, emotional, temporal, psychological experience of the here-and-now. Laura has revelations, awakenings, or epiphanies of two sorts. The first sort is expressed by her request that the dead man "Forgive my hat," and relates to her revelation that vanity and "charm" are frivolous and earth-bound whereas he is significant and spiritual. The second sort is expressed by her barely begun thought expressed to Laurie, "Isn't life..." This relates to her revelation that in the midst of music, vanity and hats, the young man brought something "marvelous" to the neighborhood in the form peace and restfulness, the form of spiritual purity, there, in the midst of darkness, gloom, and misery.