My mother attempted go on hajj more than once but was unable to go for various reasons, so I performed hajj on her behalf from her expenses while she was still alive. She was 68 years at the time and suffered from motion sickness and urinary incontinence. Please note that I had previously performed my own hajj. Is this hajj which I performed on behalf of my mother valid? 

Suleiman Ibn Yasar narrated from 'Abdullah Ibn 'Abbas that at the time of the Farewell Pilgrimage, a woman from Khuth'am approached the Prophet (may God’s peace and blessings 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" (reported by Muslim, Ahmed and others from Ibn 'Abbas, may God be pleased with them both).
The ruling
In Islamic jurisprudence, a person who cannot endure transportation is called ma'doob (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.

And God Almighty knows best.