B'resheet 21:1 Then the L-RD took note of Sarah as He had said, and the L-RD did for Sarah as He had promised.
He always keeps His Word. Here and in the future too by the future coming of the promised seed of a woman stated in Gen. 3:15.
B'resheet 21:2-4 So Sarah conceived and bore a son to Abraham in his old age, at the appointed time of which G-d had spoken to him. And Abraham called the name of his son who was born to him, whom Sarah bore to him, Yitz'chak. Then Abraham circumcised his son Yitz'chak when he was eight days old, as G-d had commanded him.
Why eight days? One reason is because blood clotting was higher then than at any other time. Another reason - It is symbolic of new beginnings.
B'resheet 21:5-7 Now Abraham was one hundred years old when his son Yitz'chak was born to him. And Sarah said, "G-d has made laughter for me; everyone who hears will laugh with me." And she said, "Who would have said to Abraham that Sarah would nurse children? Yet I have borne him a son in his old age."
Interesting. Who would have said to G-d that Miryam (Mary) would nurse His Son?
Has Miryam (Mary) born HaShem a Son in His Old age?
B'resheet 21:8-11 And the child grew and was weaned, and Abraham made a great feast on the day that Yitz'chak was weaned. Now Sarah saw the son of Hagar the Egyptian, whom she had borne to Abraham, mocking. Therefore she said to Abraham, "Drive out this maid and her son, for the son of this maid shall not be an heir with my son Yitz'chak." And the matter distressed Abraham greatly because of his son.
Ishmael scoffing - We have scoffing of G-d's plan through Yitz'chak to this day.
Here we have stress in the Home that started because of trying to force G-d's will through another. It caused chaos in the home.
Do not try to force the coming seed to fit your mold or to fit the Messiah into whom you want Him to be.
Do not try to see a Messiah accomplish only what you want Him to accomplish.
Do not try to make the Messiah into two seeds or two separate people. There will only be chaos when you do.
Throwing out of them was against the social code. (Nuzi and of Hammurabi)
Galatians 4:21-31 Tell me, you who want to be under law, do you not listen to the law? For it is written that Abraham had two sons, one by the bondwoman and one by the free woman. But the son by the bondwoman was born according to the flesh, and the son by the free woman through the promise. This is allegorically speaking: for these women are two covenants, one proceeding from Mount Sinai bearing children who are to be slaves; she is Hagar. Now this Hagar is Mount Sinai in Arabia, and corresponds to the present Jerusalem, for she is in slavery with her children. But the Jerusalem above is free; she is our mother. For it is written, "Rejoice, barren woman who does not bear; Break forth and shout, you who are not in labor; for more are the children of the desolate than of the one who has a husband." And you brethren, like Yitz'chak, are children of promise. But as at that time he who was born according to the flesh persecuted him who was born according to the Spirit, so it is now also. But what does the Scripture say? "Cast out the bondwoman and her son, for the son of the bondwoman shall not be an heir with the son of the free woman." So then, brethren, we are not children of a bondwoman, but of the free woman. NAS
Abraham followed the Spirit!