What is the big problem in the family?

The main problem for Paul's family in the short story "The Rocking-Horse Winner" is his mother's inability to love. In the first paragraph of the story, Paul's mother, Hester, is described as being a beautiful woman whose love for her husband has turned to dust. In addition to not loving her husband, Hester feels like she cannot love her children. Despite her attempts to act like she loves her children, Lawrence writes,

Only she [Hester] herself knew that at the centre of her heart was a hard little place that could not feel love, no, not for anybody (1).

Hester also believes that she has no luck, which presents another problem for her family. Despite Hester's and her husband's small incomes, she desires to maintain an elevated social status and to appear wealthy. Paul's mother equates luck with wealth and believes that she has no money because she is unlucky. Even though Paul's family lives in a nice home, there is a constant feeling of anxiety in the house. Paul naively believes that he can buy his mother's love by winning money on horse races but is unable to earn her affection and dies trying. Overall, the main source of the family's problems stem from Hester inability to love her husband and children. Paul's family also lives well above their means, and Hester's greed exacerbates the family's issues.

The big problem in the family is the mother's inability to love. We learn in the first paragraph that her love for her husband has turned to "dust" and that she cannot love her children. She has a "hard little place" in her heart where her love should be.
The mother uses money to try to compensate for not feeling love for people. She turns to money to fill the emptiness in her heart. The whole family feels the unending pressure for more money, even though they are living comfortably. The house itself seems to whisper,

There must be more money!

As we know, no amount of money can fill an empty spot in a person's heart. But Paul, being just a young boy, doesn't realize this yet. He thinks he can earn his mother's love by winning more and more money on the races. But no matter how much he wins, she wants more, and he kills himself trying to satisfy her.