How can one atone for taking money from one's mother without her knowledge and for falsely swearing upon the Qur’an?

You have committed a grave sin, which is swearing a false oath on the Qur’an. This is one of the major sins and is known as al-yamin al-ghamūs (the immersive oath), which immerses its taker in sin or the Hellfire. You could have avoided this by using equivocation in your speech. The expiation for al-yamin al-ghamūs, according to most scholars, is sincere repentance. Some have added the expiation for a broken oath. You must return the money to your mother as long as you are able.