Mrs. Greenwood is described as an emotionally detached mother who favors practicality over feeling. Esther is fundamentally different than her mother, craving the emotional warmth her mother lacks and which she had received from her father before his untimely death. Additionally, Mrs. Greenwood's resentment toward her late husband serves as a point of contention with Esther; she doesn't recall her mother crying after he died, and Mrs. Greenwood expects the children to behave in a similar fashion. Because Esther was attached to her father, she resents her mother's seeming nonchalance about his passing.
Furthermore, Esther feels alienated from her mother because of their differences. Mrs. Greenwood wants her daughter to be successful in a practical career field like she is, while Esther dreams of being a writer. Mrs. Greenwood also believes in keeping emotions held inside out of a sense of propriety, while Esther wishes her mother would lose control at least once. The measure of control that Mrs. Greenwood possesses is what Esther lacks, and perhaps one could argue that Esther is somewhat jealous of her mother's ability to maintain control.
Overall, the relationship between mother and daughter is best described as a simmering resentment rather than a volatile one. At her core, Mrs. Greenwood does care about her daughter, yet she doesn't know how to provide Esther with the kind of love her daughter wants. As a result, Esther feels kept at arm's length and unsupported.