What is Paul's mother's view of herself and her family?
The omniscient third-person narrator explains much about Paul's mother's view of herself and her family in the opening paragraph of the story.
There was a woman who was beautiful, who started with all the advantages, yet she had no luck. She married for love, and the love turned to dust. She had bonny children, yet she felt they had been thrust upon her, and she could not love them. They looked at her coldly, as if they were finding fault with her. And hurriedly she felt she must cover up some fault in herself. Yet what it was that she must cover up she never knew. Nevertheless, when her children were present, she always felt the centre of her heart go hard. This troubled her, and in her manner she was all the more gentle and anxious for her children, as if she loved them very much. Only she herself knew that at the centre of her heart was a hard little place that could not feel love, no, not for anybody. Everybody else said of her: "She is such a good mother. She adores her children." Only she herself, and her children themselves, knew it was not so. They read it in each other's eyes.
Hester has three bonny (attractive, bright, well-behaved) children, two girls and a boy. Yet she doesn't love them, and she feels guilty for not being able to so do. She does not love her husband either. It is significant that he never appears in the story. This suggests a very troubled marriage. Hester wishes he had more "luck" and could bring home more money--but even if he did bring home a lot of money, as his little son Paul manages to do, Hester wouldn't be able to love her husband any more than she loves Paul. "Only she herself knew that at the centre of her heart was a hard little place that could not feel love, no, not for anybody." This suggests that though Paul was young enough to believe that he could win her love, her husband must have realized the truth and had given up trying. He seems to be staying away from home as much as he can. Perhaps he is having an affair with another woman, though the narrator doesn't say so.
Hester loves things, not people. She loves money because of all the things it can buy. This is what prevents her from loving people, including her own family. She wants a luxurious and enviable lifestyle. She wants social prestige. One of the first things she does when she gets some of Paul's horse-racing winnings is to sign him up to attend Eton, the most prestigious prep school in England, if not in the entire world. It is the school that monarch's sons attend before going on to Oxford. In "The Rocking-Horse Winner," D. H. Lawrence seems to be echoing the words in the New Testament:
You cannot serve God and Mammon.
Hester's thoughts are always with Mammon. She reads about the doings of the upper class and nobility with admiration and envy. She yearns to have all the things and the activities they enjoy. It acts on her like a slow poison, as it does for many. It poisons her life and the lives of her husband and her children. It eventually leads to the death of her son, who never got to go to Eton because he died trying to win her love.