Making Hajj on behalf of another suffering from motion
My mother tried to go on Hajj more than once without avail. I performed Hajj on her behalf while she was still alive with her money. 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 and said, "O Messenger of Allah! 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 [pbuh] replied, "Yes, make Hajj on behalf of your father" [Reported by Muslim, Ahmed and others from Ibn 'Abbas, may Allah be pleased with them both].
In Islamic jurisprudence, a person who cannot endure transportation is called m'adub (chronically ill/ permanently disabled). Based on this, it is permissible to make Hajj on behalf of a deceased person or a weak person. If the case is indeed as mentioned in the question, the Hajj you performed on behalf of your mother is valid.
Allah Almighty knows best.