Rabbi Yehuda says that that the night G-d spoke to Abraham, saying: "Abraham! What Sarah told you is true. " Abraham got up early in the morning and wrote a letter of divorcement and gave it to Hagar and expelled her (and her son) from him and from Isaac his son, from this and future worlds, as it says, "And Abraham got up early in the morning and took the bread and a skin of water ... "(ibid. 14) and tied it to her belt that dragged behind her for all to see that she was a slave woman and that if he wanted, he could find his son Ishmael by the trail that the skin left on the ground so that everyone would know that she was still his slave". Thus Abraham could still visit them and in the merit of Abraham, water was not depleted in the skins.
But when Hagar got to the desert and started worshiping idol of her father's house, the water immediately stopped. It was then that it was revealed to them the source of water which was established with the creation of the world - before the first Sabbath. "And they went and drank, and filled the skins" – this is Miriam‘s Well from which the Jews in the desert drank water but the first to drink from it was Ishmael!
Ishmael took a wife from Moab named Isa. Three years later, Abraham went to visit Ishmael. Before he left, he swore to Sarah that he would not get off the camel. When Abraham got to where Isamel was living, he met his wife and asked: Where is Ishmael?
She replied: He went with his mother to bring grain and dates from the desert.
Abraham responded: Give me a little bit of water and a bit of bread, I’m very tired from the trip through the desert.
She replied: No bread and no water.
Abraham said to her: When Ishmael returns, tell him that an old man from Canaan was visiting and said that the doorpost at home is in bad shape.
When Ishmael came, his wife told him what had occurred and he kicked her out. Then he sent his mother to look for a wife for him and she took him a wife from her father's house and her name was Ptuma. After another 3 years, Abraham went back to visit his son Ishmael. When he arrived, he asked Ptuma: Where is Ishmael?
She replied: He went with his mother to feed the camels in the desert.
Abraham then said to her: Give me a little bit of water and a bit of bread, very tired is my soul because of the trip through the desert.
She did and then Abraham stood up and prayed for Ishmael and his house was filled with all good things and blessings. When Ishmael came home, his wife told him everything, and he realized that his father still loved him.
Our Sages tell us a Jew, even though he may sin, remains a Jew whereas Ishmael, when separated from the source, loses merit. All his power is based on belonging to the faith of Abraham and his connection to the aspect of Chesed (kindness).
Thus we see that it is not sufficient to assume that all our strength lies in the fact that a Jew, in spite of sin, is always a Jew. Jews must act more like Abraham’s true offspring and the more this is done, the quicker will Ishmael will be driven out of this and future worlds.