Should she do Hajj and give charity on behalf of her mother who did not pray?

The one who does not pray because he denies that it is obligatory is a kaafir according to scholarly consensus. The one who does not pray out of negligence and laziness is a kaafir according to the more correct of the two scholarly opinions, because the Prophet (peace and blessings of Allaah be upon him) said: “The covenant that stands between us and them is prayer; whoever gives it up is a kaafir.” And there is other evidence to that effect from the Qur’aan and Sunnah. Based on that, it is not permissible to do Hajj or give charity on behalf of someone who has died and did not pray, just as it is not permissible to do Hajj and give charity on behalf of any other kaafir. 

And Allaah is the Source of strength. May Allaah send blessings and peace upon our Prophet Muhammad and his family and companions. End quote. 

Standing Committee for Academic Research and Issuing Fatwas 

Shaykh ‘Abd al-‘Azeez ibn Baaz, Shaykh ‘Abd al-Razzaaq ‘Afeefi, Shaykh ‘Abd-Allaah ibn Qa’ood.