In "The Rocking-Horse Winner," how does the boy’s mistake about the "filthy lucker" clarify his mother's thinking?And her motivations

Paul misunderstands what his uncle has said: although he hears the words "filthy lucker," the expression is "filthy lucre."  Lucre means monetary reward or gain. 

"Oh ! " said Paul vaguely. "I thought when Uncle Oscar said  filthy lucker, it meant money."

"Filthy lucre does mean money," said the mother,   "But it's lucre, not luck."

"Oh ! " said the boy. "Then what is luck, mother?"

"It's what causes you to have money. If you're lucky you have money. That's why it's better to be born lucky than rich. If you're rich, you may lose your money. But if you're lucky, you will always get more money."

Paul's father, according to his mother, has neither luck nor money.  And for this reason, she has become very bitter. 

Paul has it right. His luck is "filthy" and the money is filthy as well, for greed is destroying his family, so much so that his mother will be blinded to even the death of her own son in order to reap the filthy lucre.