Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
First of all we congratulate the dear questioner for his adherence to the obedience of his mother. We ask Allah to put him among the obedient people in paradise.
As for sending the reward of the Qur'an recitation to a living or dead Muslim, there is no objection to it.
Imam Al Hijjawy said: "Any good act that brings the person nearer to Allah and which he does with the intention that its reward reaches a living or dead Muslim, it benefits him (the person to whom it is sent)."
Imam Ahmed said: "All good deeds done on behalf of a dead person reach him/her ". The Hanafis believe that the Qur'an recitation reaches the dead person.
This is also the opinion of the Hambali and some of the Shafi'e.
So, there is no objection to your reading the Qur'an with the intention that its reward reaches your living mother.
Allah knows best.