I mistakenly put Xbox Live points on my profile and want my son to be able to use the points.
He has Xbox Live Gold, I have Xbox Live free.
We are on the same console.
The Xbox Live points are tied to your profile. He cannot use them from his.
The good news is the content purchased with the points is licensed to the console it was bought on. This means you or your son can purchase content through your account and he will still be able to access it from his.