He is going to form the intention to do a second ‘umrah when he is in Jeddah; where should he enter ihram from?

Firstly: 

What is required of the one who sets out for Makkah to perform Hajj or ‘Umrah is to enter ihram from the miqaat that he passes through or comes in line with. It is not permissible for him to go beyond that point without entering ihram. If he is closer [to Makkah] than that, then his miqaat is the place from which he sets out, because the Prophet (blessings and peace of Allah be upon him) said, when he defined the miqaats: “They are for them and besides them for those who come through those places with the intention of performing Hajj and ‘Umrah; and whoever is living within these boundaries can enter ihraam from the place he sets out, and the people of Makkah can start from Makkah”

Narrated by al-Bukhaari (1524) from the hadeeth of Ibn ‘Abbaas (may Allah be pleased with him). 

Based on that, what you must do is enter ihram from the miqaat through which you pass or with which you come in line on your way from al-Jawf to Makkah. 

The scholars of the Standing Committee said: 

Whoever passes through one of the miqaats that are proven from the Messenger of Allah (blessings and peace of Allah be upon him) or comes in line with it by air or land or sea, intending to perform Hajj or ‘Umrah, it is obligatory for him to enter ihram. If he is not intending to perform Hajj or ‘Umrah, then he does not have to enter ihram. If he passes it without intending to perform Hajj or ‘Umrah, then he sets out for Hajj or ‘Umrah from Makkah or Jeddah, then he should enter ihram from wherever he sets out from in Makkah or Jeddah, for example. In the case of ‘umrah, if he sets out for it from outside the Haram zone, he should enter ihram for it from where he sets out, but if he sets out for it from within the Haram zone, he has to go out to the nearest point outside the Haram zone and enter ihram from there for ‘Umrah. This is the basic principle with regard to this matter. End quote. 

Fataawa al-Lajnah ad-Daa’imah (11/122) 

Secondly: 

With regard to the second ‘umrah that you are intending to do from Jeddah, you can enter ihram for it from Jeddah, and you do not have to go to at-Tan‘eem, because at-Tan‘eem is not specified as a place to enter ihram. Rather it is a place outside the Haram zone to which a resident of Makkah goes to in order to enter ihram for ‘umrah, but if he goes out in a different direction beyond the Haram zone and enters ihram for ‘umrah from there, that is valid. 

Shaykh Ibn Baaz (may Allah have mercy on him) said: 

If a person wants to perform ‘umrah from Makkah, he should go out of the Haram zone and enter ihram from there, such as at-Tan‘eem, al-Ji‘raanah and so on, because the Prophet (blessings and peace of Allah be upon him) instructed ‘Aa’ishah, when she was in Makkah and wanted to perform ‘umrah, to go out to at-Tan‘eem and enter ihram from there. End quote. 

Majmoo‘ Fataawa Ibn Baaz (17/41) 

If a person goes out to Jeddah, and wants to perform ‘umrah, he may enter ihram from Jeddah. 

The scholars of the Standing Committee also said: 

If you set out for ‘umrah from Jeddah, then enter ihram from Jeddah. 

End quote from Fataawa al-Lajnah ad-Daa’imah (11/136) 

Shaykh Ibn Baaz (may Allah have mercy on him) said: 

Jeddah is not a miqaat for those coming from further afield; rather it is a miqaat for those who live there and for those who come there not intending to do Hajj or ‘Umrah, then they set out for Hajj and ‘Umrah from there.

End quote from Majmoo‘ Fataawa Ibn Baaz (17/34) 

Thirdly: 

Doing a second ‘umrah on the same day or soon after doing your first ‘umrah is not in accordance with the Sunnah and it was not the practice of the early generations; rather your first ‘umrah that you did from al-Jawf is sufficient for you. 

If you want to do your ‘umrah with your mother, then you can delay your ‘umrah; you can come from al-Jawf and enter ihram at the miqaat at which the people of al-Jawf enter ihram, then go to Jeddah and meet your mother, and you can delay your ‘umrah so that you can accompany her. 

Shaykh al-Islam (may Allah have mercy on him) said in Majmoo‘ al-Fataawa (26/45): 

Hence the more correct view according to our companions is that which was narrated from Ahmad, that he did not regard it as mustahabb to do ‘umrah repeatedly, either from Makkah or elsewhere. Rather there should be a period of time between each two ‘umrahs, even if it is only enough time for his hair to regrow so that he will be able to shave it. End quote. 

See also the answer to question no. 111501

And Allah knows best.