Is repentance and expiation obligatory for one who breaks his oath by returning to disobedience after swearing on the Qur’an to abandon it, and is it permissible to pay the expiation from the mother's money, given the financial circumstances?

You are not required to offer expiation for committing the sin forgetfully after swearing the oath. However, committing it deliberately and remembering the oath twice necessitates a single expiation for the oath. Since you are a student and cannot afford to feed or clothe, you must fast for three days as expiation.

The emphasis of an oath by placing a hand on the Qur’an has not been authentically reported from the Prophet, peace and blessings be upon him, nor his Companions; rather, it is an innovation. The oath is concluded by the swearing itself.

Allah accepts repentance from His remorseful servants. If you show Allah sincerity in turning to Him, He will assist and guide you. To soften the heart and moisten the eye, you must engage in acts of obedience, abandon sins, seek good companionship, attend circles of knowledge, recite morning and evening remembrances, have a daily portion of Qur’an, and perform night prayers and fasting. Beware of despairing of Allah's mercy, and hasten to sincere repentance.