The whole problem in "The Rocking-Horse Winner" stems from the fact that Paul's mother cannot love her children because she is incapable of loving anybody. She tries to be a good mother, and she pretends to love all three of her children; but, as the narrator explains it, there is a hard place in the center of her heart which prevents her from loving. The children are all aware of it.
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.
Paul is desperate to gain his mother's love. He gets the idea from a conversation he has with her that she would love him if only, unlike his father, he was "lucky." According to the "Summary" in the enotes study guide for "The Rocking-Horse Winner":
Paul clearly accepts the unspoken invitation to take his father’s place in fulfilling his mother’s dreams of happiness.
Either through some mysterious, supernatural, and possibly malignant force or else merely through an unusual streak of luck, Paul begins making money by picking winning horses at important upcoming thoroughbred races. He places the bets through Bassett the gardener, who was the person who got him interested in horse-racing. Together they accumulate a great deal of money, and then they bring Paul's Uncle Oscar into their secret. Uncle Oscar is indispensable because he arranges the anonymous transfers of money from Paul to his mother.
Paul manages to give his mother five thousand pounds out of his winnings without her knowing the source of the money. But this doesn't buy him any more of her love. It only whets her desire for more money.
There were flowers in the winter, and a blossoming of the luxury Paul's mother had been used to. And yet the voices in the house, behind the sprays of mimosa and almond-blossom, and from under the piles of iridescent cushions, simply trilled and screamed in a sort of ecstasy: "There must be more money! Oh-h-h; there must be more money. Oh, now, now-w! Now-w-w - there must be more money! - more than ever! More than ever!"
The story never makes it clear whether Paul just happens to be on a winning streak or whether there is something supernatural involved in his being able to learn the names of future winning horses if he rides his rocking-horse long enough and hard enough. Eventually he kills himself with his exertions, but it is evident at the end that his mother still does not love him. She accepts his death without any apparent display of maternal grief. It is pitifully ironic that the dying boy considers himself "lucky."
"I never told you, mother, that if I can ride my horse, and get there, then I'm absolutely sure - oh, absolutely! Mother, did I ever tell you? I am lucky!"
"No, you never did," said his mother.
But the boy died in the night.