Praise be to Allah.
The proxy does not have to do Hajj from the same town as the one on whose behalf he is doing Hajj, and he does not have to enter ihraam from his meeqaat, rather the proxy should enter ihraam from his own meeqaat. There is nothing wrong with performing Hajj from Jeddah on behalf of a woman from Yemen, and the proxy may enter ihraam from Jeddah.
The Standing Committee for Issuing Fatwas was asked about a man from Africa who wanted to delegate someone to do Hajj on behalf of his mother, and they replied:
It is permissible for the person mentioned to appoint a trustworthy person from Makkah or elsewhere to do Hajj on behalf of his mother if she is deceased or is unable to do Hajj herself, because she is elderly or sick with no hope of recovery.
And Allah is the Source of strength. May Allah send blessings and peace upon our Prophet Muhammad and his family and companions. End quote.
Standing Committee for Academic Research and Issuing Fatwas.
Shaykh ‘Abd al-‘Azeez ibn ‘Abd-Allah ibn Baaz, Shaykh ‘Abd al-Razzaaq ‘Afeefi, Shaykh ‘Abd-Allah ibn Ghadyaan, Shaykh ‘Abd-Allah ibn Qa’ood.