"But Sarah saw that the son whom Hagar the Egyptian had borne to Abraham was mocking, and she said to Abraham, 'Get rid of that slave woman and her son, for that woman's son will never share in the inheritance with my son Isaac.'" NIV translation
Although we do not know exactly what Ishmael was doing, we see that there was tension between him and Isaac. At this time, Ishmael would have been a teenager and was picking on Isaac. It seems harsh but Sarah tells Abraham that they must go and that Ishmael will not share in Isaac's inheritance. This reveals the heart of the matter and the problem that continues to this day. Ishmael was a child of man's efforts as it was Abraham & Sarah's plan to have a child through Hagar. God's plan was for them to have a son through Sarah but they had grown impatient and taken matters into their own hands.
This struggle between man's efforts and God's plan continues even in the hearts of believers. Sometimes, we find it hard to believe that all we have to do is put our trust in the Lord and not try to work for our salvation.
"The matter distressed Abraham greatly because it concerned his son. But God said to him, Do not be so distressed about the boy and your slave woman. Listen to whatever Sarah tells you, because it is through Isaac that your offspring will be reckoned. I will make the son of the slave into a nation also, because he is your offspring.'" NIV translation
The thought of sending his own flesh and blood (Ishmael) away was tearing him up and God showed up to speak to Abraham.
He was told that what Sarah was saying was true and was His will. He also comforted Abraham by telling him that Ishmael would be a nation as well.
Here, we have the root of the problem between Islam and Jews. Ishmael would become the father of a nation based on man's efforts (Islam) while Isaac would become a nation of promise (Judaism). The Jews were promised a Messiah and that Messiah was and is Jesus Christ.
"Early the next morning Abraham took some food and a skin of water and gave them to Hagar. He set them on her shoulders and then sent her off with the boy. She went on her way and wandered in the Desert of Beersheba." NIV translation
Abraham listened to the Lord and sent Hagar and Ishmael away. We notice that he provided them with food and water and that reminds us that their descendants also have the opportunity of accepting Jesus Christ and returning to the family of God.
Imagine the feelings of rejection and anger that this teenage boy must have felt. This damaged pride is the root of the problem and what the devil has used to great advantage in our world today. Today, it has progressed from mocking to murder but the cause is still pride. The answer is Jesus as He is the Prince of Peace and the only way to reconcile this broken family.