All praise is due to Allah alone, and may the Salah and Salam of Allah be upon our Prophet Muhammad, his family and his companions. To answer your question, we say while seeking all the success from Allah: Hajj al-Tamattu' is to enter the state of ihram to do Umrah during the months of Hajj and then after completing the rituals of Umrah, beginning the rites of Hajj on the day of Tarwiyah (i.e. the eighth day of Dhul-Hijja). Thus, the Umrah you intend to do on behalf of your mother is considered part of the acts of Hajj al-Tamattu'. Your brother, Khalid al-Mosleh 24/11/2014