In "The Rocking-Horse Winner" what secrets do the various characters keep from one another?
All the major character is "The Rocking-Horse Winner" keep secrets. Hester does not love her children but she acts as if she does. She keeps this secret that she does not love them. In spite of this, the children seem to know the secret:
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 keeps another secret from Paul by omission. She explains to him that luck "causes you to have money." Hester is not really keeping a secret per se, but she is giving Paul a limited view about what "luck" means. Since she is so focused on money, she omits that luck or good fortune might involve other things: love, family, health, etc.
Paul, in a generous attempt to surprise his mother with money ("luck"), kept it a secret that he could predict the winners of horse races by riding his nameless rocking-horse. Oscar and Bassett also keep this to themselves, not telling Hester or Paul's father. "Paul's secret of secrets was his wooden horse, that which had no name." It wasn't until the end, just before he died, that he admitted he was "lucky."
The more troubling secret that Hester keeps from Paul and others is that she spends all of Paul's winnings on things for the house (and, presumably, a fur coat for herself). Rather than pay her debts, she spends the money selfishly and frivolously.
Hester did express concern for her children but she did not love them and she was preoccupied with money. So, it's difficult to say whether or not she would have thanked Paul or intervened if she had known he was responsible for giving her the money.