In Mrs. Dalloway by Virginia Woolf, the importance of motherhood to Mrs. Dalloway is that, in some ways, motherhood gives her life a sense of purpose. She says,
Sometimes lately it had seemed to her that, except for Elizabeth, her food was all that she lived for; her comforts; her dinner, her tea; her hot-water bottle at night.
However, she does not spend much time at all with her daughter. However, her daughter is almost a trophy for her to display at her parties, as if to show that she has fulfilled all the requirements that a well-bred woman of her generation must: she entered into marriage with a wealthy man, she gave birth to a child, and she is a consummate hostess, giving lots of parties.
In fact, not only does Mrs. Dalloway not spend much time with Elizabeth, she seems not to really know her daughter well at all. She marvels that Elizabeth does not care for gloves or parties. The only thing that “Elizabeth really cared for [was] her dog most of all.”
Mrs. Dalloway is also jealous of Elizabeth’s relationship with Doris Kilman, but it does not seem that the jealousy stems from Mrs. Dalloway’s love for her daughter and desire to spend time with her herself. Rather, the jealousy seems to come from what she views as the gauche religious practices that Elizabeth and Doris do together, including attending Communion and praying.
Much of her relationship with her daughter, then, seems to be for show. In other words, because Elizabeth does not care “how she dressed, how she treated people who came to lunch,” it reflects badly on Mrs. Dalloway’s projected success or how she believes other people perceive her in terms of how well she raised Elizabeth. That is likely the main reason that she is not happy with Elizabeth's relationship with Doris.
She feels very proprietary about Elizabeth. When Clarissa's old beau Peter comes to see her, she introduces Elizabeth as “my Elizabeth.” This is less to show a sense of pride in her daughter but more to show Peter how well she has fared in the years that they have been apart. After all, she is a wife and a mother.
Here is my Elizabeth," said Clarissa, emotionally, histrionically, perhaps.
Peter thinks that the way she said "Here is my Elizabeth!" was insincere, and it probably was.