All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
The Muslim who has already performed his obligatory Hajj can perform Hajj on behalf of someone who cannot perform his/her Hajj due to his death, or aging, or chronic illness when there is very little hope of recovery. There are sound Ahadeeth supporting the above ruling. Ibn ‘Abbas narrated that a woman from the tribe of Khath'am came to the Prophet and said: “O Messenger of Allah! My father has come under Allah's obligation of performing Hajj but he is a very old man and cannot sit properly on his mount. Shall I perform Hajj on his behalf? The Prophet replied in the affirmative.” [Al-Bukhari]
There is no difference between parents or others concerning this ruling. Ibn ‘Abbas, Allaah be pleased with him, narrated that the Prophet heard a man saying: "'Labbayk on behalf of Shubrumah.’ He asked: 'Who is Shubrumah'? He replied: 'A brother or relative of mine'. He asked: 'Have you performed Hajj on your own behalf?' He said: ‘No.’ Thereupon, the Prophet said to him: ‘Perform Hajj on your own behalf, then perform it on behalf of Shubrumah.” [Abu Dawood and Ibn Maajah]
Therefore, you should know that appointing someone who has already performed his Hajj to perform Hajj on behalf of your dead mother is permissible.
Allah knows best.