1- Believer should submit completely to the commands of Allaah The Almighty, prefer His obedience and love to all other things even if his righteous wife and sole son. As we see, Ibraaheem carries out the commands of Allaah The Almighty when He commanded him to take his wife (Haajr) and her little child to an uncultivated valley that has no human being nor provision.
2- Haajar, may Allaah exalt her mention, was very obedient to her husband and had firm belief in her Lord, put her full trust in Him, showed great patience, accepted to live in an uncultivated valley that has no humans nor provision after she knew from Ibraaheem, may Allaah exalt his mention, that Allaah The Almighty ordered him to left them in this valley as it is mentioned in the Hadeeth: "Then Ibraaheem, may Allaah exalt his mention, set out homeward. Ismaa‘eel's mother followed him saying, "O Ibraaheem! Where are you going, leaving us in this valley where there is no person whose company we may enjoy, nor is there anything (to enjoy)?" She repeated that to him many times, but he did not look back at her. Then she asked him, "Has Allaah The Almighty ordered you to do so?" He said, "Yes." She said, "Then He will not neglect us," and returned."
This really sets a good example of the righteous woman that responds to the command and decree of Allaah The Almighty and helps her husband to worship Him The Almighty.
3- Ibraaheem left his faithful wife and his little child in a valley after giving them a leather bag containing some dates, and a small water-skin containing some water and then supplicated Allaah The Almighty for them saying: "O our Lord! I have made some of my offspring dwell in a valley without cultivation, by Your Sacred House". In this way, Ibraaheem, may Allaah exalt his mention, teaches us to combine between Du‘aa' (i.e. supplicating Allaah The Almighty) and adopting permissible possible methods.
4- Allaah The Almighty ordered those who perform Hajj and Umrah to walk between As-Safa and Al-Marwah to remind them with what occurred to their mother Haajar. Accordingly, this act becomes a ritual act until the Day of Resurrection with which believers do so as to come closer to Allaah The Almighty.
5- Islmaa‘eel's Mother, may Allaah exalt her mention, searched for water when she had ended up, applied the permissible possible means and walked between As-Safa and Al-Marwa several times until Allaah The Almighty gave her and her child the water of Zam-Zam.
6- Allaah The Almighty never allow to be lost the reward of any who did well in deeds, where Ibraaheem, may Allaah exalt his mention, left his family in Makkah acting upon the commands of his Lord, believing in Him and putting his trust in him while there is no any human being there at that time. Allaah The Almighty did not neglect his family; rather, He provided them from His Bounties and made the well of Zam-Zam gush out for them. Its water is very blessed and from which people will drink until the present time. He The Exalted also brought to them some people from the tribe of Jurhum to live with them so that they may have friendship with them and their loneliness may dissipate.
7- It is permissible for one to seek help from others regarding whatever in their abilities as Ismaa‘eel's mother, may Allaah exalt her mention, did. As for seeking help from the dead or the absent or what is beyond the power of humans, then this is not permissible and implies Shirk (i.e. polytheism).
8- Allaah The Almighty chose the family of Ibraaheem, may Allaah exalt his mention, and made from his offspring prophets and messengers, then how Ibraaheem can accept a wife for his son that does not live for her spiritual needs and only lives to her physical needs. Does not care except about food and drink. She disdained her guest; the father of her husband, denied the blessings of her Lord, complained her way of living. Therefore, Ibraaheem, may Allaah exalt his mention, advised his son Ismaa‘eel, may Allaah exalt his mention, to divorce her.
9- The second wife of Ismaa‘eel, may Allaah exalt his mention, respected her guest, thanked the graces of her Lord and thus Ibraaheem, may Allaah exalt his mention, advised his son to keep and take care of her.
10- Obedience and patience have great results and everlasting memory. The desolate place in which Haajar, the mother of Ismaa‘eel, may Allaah exalt her mention, descended while it is desert and uncultivated, became afterwards a sacred ritual and inhabited place in which there is a blessed water (Zam-Zam), to which the hearts of many people incline, different fruits are given and groups of pilgrims from all over the world come to it to witness the benefits of the worldly life and Hereafter.
11- Good education and disciplining have a great effect on having good children, after actually the guidance of Allaah The Almighty. This was very evident in the submission of Ismaa‘eel, may Allaah exalt his mention, to the orders of his father Ibraaheem, may Allaah exalt his mention, in divorcing his wife and helping him to build the Ka‘bah and even before that when his father said to him (as Allaah The Almighty says on his behalf): {"O my son! I have seen in a dream that I am slaughtering you (offer you in sacrifice to Allaah), so look what you think!" He said: "O my father! Do that which you are commanded, Inshaa' Allaah (if Allaah will), you shall find me of As-Sabireen (the patient ones, etc.)."} [Quran 37: 102]
12- It is permissible to ask Allaah The Almighty to accept the good deeds. Ibraaheem, may Allaah exalt his mention, has built the Ka‘bah with his own hands and Ismaa‘eel, may Allaah exalt his mention, gave him stones while they supplicating Allaah The Almighty to accept such deeds from them. Allaah The Almighty Says (what means): {And (remember) when Ibraaheem and (his son) Ismaa‘eel were raising the foundations of the House (the Ka‘bah at Makkah), (saying), "Our Lord! Accept (this service) from us. Verily! You are the All-Hearer, the All-Knower." "Our Lord! And make us submissive unto You and of our offspring a nation submissive unto You, and show us our Manaasik (all the ceremonies of pilgrimage - Hajj and 'Umrah, etc.), and accept our repentance. Truly, You are the One Who accepts repentance, the Most Merciful.} [Quran 2: 127-128]
Allaah The Almighty accepted their invocations, gave them great honor and grant them high degrees.