Answer
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
1- It is permissible to make hajj on behalf of a deceased or weak person.
2- If your mother is suffering from motion sickness or urinary incontinence, the hajj you performed on her behalf is valid.
Answering your question, Dar Al-Ifta Al-Misriyyah, states:
Sulayman Ibn Yasar narrated from `Abdullah Ibn `Abbas that at the time of the Farewell Pilgrimage, a woman from Khuth`am approached the Prophet (peace be upon him) and said, “O Messenger of God! My father is an old man. He cannot sit firmly on his mount and therefore cannot perform his obligatory hajj. Would it fulfill the obligation if I make hajj on his behalf?” The Prophet replied, “Yes, make hajj on behalf of your father” (Muslim, Ahmad and others)
In Islamic jurisprudence, a person who cannot endure transportation is called ma`dub (one who is chronically ill/ permanently disabled).
Based on this, it is permissible to make hajj on behalf of a deceased or weak person. If the case is indeed as mentioned in the question, the hajj you performed on behalf of your mother is valid.
Almighty Allah knows best.
Source: http://www.dar-alifta.org/Foreign/ViewFatwa.aspx?ID=1371&text=hajj