All perfect praise be to Allaah, the Lord of the Worlds. I testify that there is none worthy of worship except Allaah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
In fact, performing Hajj on behalf of a dead mother or father is one of the greatest righteous acts that can bring one closer to Allah, the Exalted. The Prophet, sallallaahu ‘alayhi wa sallam, said to Abu Razeen : "Perform Hajj and ‘Umrah on behalf of your father." [Ahmad, Abu Daawood, An-Nasaa’i, At-Tirmithi, and Ibn Maajah]
Moreover, a woman asked the Prophet, sallallaahu ‘alayhi wa sallam, "My mother died, and she had not performed Hajj; can I perform Hajj on her behalf?" The Prophet, sallallaahu ‘alayhi wa sallam, replied, "Yes, perform Hajj on her behalf." [At-Tirmithi and Al-Albaani: Saheeh]
Whoever wants to perform ‘Umrah on behalf of his dead or disabled parents, or for one of them, should perform a separate ‘Umrah for each of them. It is invalid to combine the intentions of performing the ‘Umrah for more than one person or for himself and another person.
This is because performing ‘Umrah is an independent act of worship, and it is invalid to perform a single ‘Umrah with two intentions. Ibn Qudaamah wrote:
If two persons authorized another to perform ‘Umrah /Hajj on their behalf and he assumed the state of Ihraam with the intention of performing ‘Umrah for them both, it (‘Umrah/Hajj) would count for himself only, not for any of them because ‘Umrah/Hajj cannot be performed on behalf of both of them at the same time. [Al-Mughni]
This indicates that it is invalid to assume Ihraam for (a single) Hajj/‘Umrah in favor of more than one person.
Therefore, we advise the questioner to perform ‘Umrah first for herself or her mother and then end the state of ihram and go to the miqat (At-Tan‘eem) to assume a new state of ihram for the second ‘Umrah for herself or her mother or any other person. This is of course if she had already performed the obligatory ‘Umrah for herself; otherwise, she should perform ‘Umrah for herself first.
Whoever wants to perform Hajj or ‘Umrah on behalf of someone may set off from any country he wishes, and not necessarily from the country of the person on whose behalf the Hajj or ‘Umrah is performed. This is according to the correct view on this regard.
Allah Knows best.