Why is Wilde's treatment of women different in A Woman of No Importance and The Picture of Dorian Gray?
This is a great question because there is, indeed, a difference in the treatment, the descriptions, and the roles of women from one work to the other. In Dorian Gray the roles of women are of temptresses and lovers, for which Wilde had a special dislike. In A Woman of No Importance, the role is less romantic and more nurturing, for which there is no need for Wilde to give any negative treatment. Hence, we will see how in the novel, Dorian Gray, the negative treatment much more brutal by far.
In the novel The Picture of Dorian Gray the main character of Dorian uncovers his inner demons and clearly intends to live a life of "sensations". His hedonism is admired throughout the narrative, as well as the equally hedonistic nature of Lord Henry Wooton. This hedonism has huge homoerotic undertones that, by default, make any female character basically out of place with the rest of the plot. From the way in which females are depicted in Dorian Gray, we get the impression that Wilde wants every man in Victorian London to dislike women altogether. He does this through the physical and psychological characterization of Victoria Wooton and the description of the behaviors of Sybil Vane.
For example, he says of Victoria, Lady Henry Wooton, in chapter IV of The Picture of Dorian Gray
She was a curious woman, whose dresses always looked as if they had been designed in a rage and put on in a tempest. She was usually in love with somebody, and, as her passion was never returned, she had kept all her illusions. She tried to look picturesque, but only succeeded in being untidy. Her name was Victoria, and she had a perfect mania for going to church
Later, in chapter VII, Dorian literally destroys Sybil Vane's oath of eternal love for him only because she is too much in love with him to be able to do her job and act well on stage. The words that he says to her provoke her suicide, and with good reason:
[...] you have killed my love. You used to stir my imagination. Now you don't even stir my curiosity. You simply produce no effect. I loved you because you were marvelous, because you had genius and intellect, because you realized the dreams of great poets and gave shape and substance to the shadows of art. You have thrown it all away. You are shallow and stupid.
Hence, both women are depicted under such a spiteful and distasteful light that one wonders whether Wilde already had his homosexual inclinations on check or whether he was in the process of discovering them.
In A Woman of No Importance women do not have a romantic role, per se. However, Mrs. Arbuthnot is a wronged woman who wants to save her son from the public shame of knowing that she had him out of wedlock. Therefore, Wilde treats the female characters best when they are in motherly or nurturing roles as opposed to roles roles in which they are lovers. It may be a direct similarity to Wilde's love for his own mother, compared to other women, who inspires him to write better of them this way. Even Mrs. Arbuthnot language is nearly angelical.
Leave me the little vineyard of my life;
leave me the walled-in garden and the well of water; the ewe-lamb God sent me, in pity or in wrath, oh! leave me that. George, don't take Gerald from me.
Therefore, the treatment of women in A Woman of No Importance, though old-fashioned, is way more effective and believable.