The secrets Paul keeps from his mother are: (1) he earns money for her by riding his rocking horse furiously to determine the future winners of races and (2) that he is lucky.

Paul tried to tell his mother that he is lucky; they have a conversation about the difference between lucre and luck. His mother explains to Paul that luck is what brings you lucre (or money). When Paul tells his mother that he is lucky, she laughs at the idea and dismisses it.

Paul gives his mother the five thousand pounds he earned (by having Bassett place bets for him on the races), but he has the money sent to her anonymously. She has no idea it comes from her son. He says he wants it done this way:

I shouldn't like mother to know I was lucky.

His mother doesn't know until it is too late that her son is riding the rocking horse furiously in order to win vast sums of money for her.

You are correct in your assumption here. Clearly in the tale there are two secrets going on - the more overt, clearly narrated one about Paul and his betting with Basset and Uncle Oscar, but then there is the deeper, more supernatural secret that is kept even from Basset and Uncle Oscar. It is evident that Paul is only able to discern the names of the up and coming winners of horse races thanks to his frenzied, demonic rides that eventually drive Paul to his fevered death. The rocking horse then itself becomes the focus of this "secret within a secret". It is well worth asking yourself what you think the rocking horse might symbolise. Teaching this story recently I asked my students the same question and they came up with the following responses: luck, demon possession, attempt to gain perfection, evil, greed, materialism. So take your pick!