My mother died last year and I want to know if it is right or wrong to visit her tomb and read Qur'an for her, please provide details.

Praise be to Allah, the Lord of the Worlds; and blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

Muslim scholars have various opinions concerning the issue of women visiting graves. For details refer to fatwaNo:81272.
As for reciting Qur'an on graves as practiced in some countries, people hire someone to recite Qur'an, or they personally intend visiting graves for merely reciting Qur'an. This practice is not conform to Sunnah and thus would be considered Bidah, because the known way of the Prophet concerning visiting graves was that he used to greet them Saying
(Peace be upon you all. O inhabitants of the graves, amongst the believers and the Muslims. Verily we will, Allah willing, be united with you, we ask Allah for well being for us and you). Then he makes Du'a for the dead persons.
On the other hand, reciting Qur'an for a dead person and presenting its reward to him is permissible according to the majority of the Muslim scholars. This is the opinion of Shafites, Hanbalites and Hanafees. The Malikites disliked it.
If you recite Qur'an with the intention of sending its reward to a dead person there is no harm in doing so, but it is more appropriate to supplicate for the dead person, instead of presenting the reward of reciting Qur'an, as it is the sound way of the Sunnah avoiding thus any doubt of Bidah.
Allah knows best.