Mademoiselle Reisz is an older woman with great artistic attributes who chooses to live her life against the conventions of her generation. Rather than marrying, bearing children, and living a "righteous" life, she follows her artistic passion, forfeits any social expectation bestowed upon her, and leads a carefree and presumably happy life on her own. She is the center of her own world, and she is, as such, quite in tune with who she is as a person. She also serves as Edna's key listener in all matters related to Robert. After all, it is Reisz who has the most contact with him, and Edna depends on her to hear from Robert.
This makes it not surprising that Edna, who is undergoing a deep identity crisis, is drawn to Reisz, seeing in her the woman she (Edna) could potentially become if she, too, had the courage to go against conventions and follow her own passions. While the women are not necessarily too emotionally bonded with one another, Edna could have desired to lead a life like Reisz's. Eventually, Edna emulates the key traits of Reisz's life when she moves to the "pigeon's hole" and attempts to lead a free life as well.
On the other hand, Adéle Ratignolle is the exact opposite of Reisz. She is married, a devoted mother, and she consistently reminds Edna about the importance sacrificing and doing everything for the children. While Reisz is open to discuss Robert with Edna, Ratignolle strongly encourages her against any inappropriate behavior. Moreover, Reisz is a constant reminder to Edna that, no matter how badly she tries to escape her husband or children, her passions are her primary trap. Edna's infatuation with Robert and her desire to be free continue to clash with the reality of her still being a wife and mother who is expected to behave as such. Adele is perhaps a guilt factor in Edna's life.
Therefore the two women represent the two extremes that pull Edna to the edge. Reisz is the part of Edna that wants to be free, start over, and see the world through passion, not conventions. Ratignolle represents the part of Edna that she dislikes the most: the proverbial sacrificial mother and wife that she had no other choice but to become. Still, Edna sees parts of herself in both women and realizes that she may not ever find a happy medium. Frustrated, Edna will eventually end her own life as a result of her overall dissatisfaction with life.
Mme. Ratignolle shows the society's view of women as mothers. Her advice to Edna is to "remember the children." Ratignolle is loving and nurturing, but devoid of independence or personality. Mlle. Reisz, though, is living her life as she desires, not caring what society thinks of her. She is able to be extravagant and lavish, fully embracing her artistic capabilities because she does not have other obligations. She denies society's structure, and encourages Edna to do the same. This free lifestyle is what Edna comes to desire and seek for herself.