Was Hagar's return necessary?

Sarai was barren and could not bear a child to inherit Abram's estate. She proposed to give Hagai her maid to Abram as a wife to bear him an inheritor. After Hagai had been conceived, she did not respect her mistress.
And he went in to Hagar, and she conceived; and when she saw that she had conceived, she looked with contempt on her mistress (Genesis 16:4).
Sarai complained to Abram who took an action incomprehensible to us Chinese. He did not defend his gene and allowed Sarai to do whatever she pleased. Sarai treated Hagai harshly and she fled (Genesis 16:6). After receiving a promise from God, Hagai returned to Sarai and submitted to her. It was necessary for Hagai to return because she was a slave. She must return to her mistress. That was the custom of the day.
The angel of the LORD said to her, "Return to your mistress, and submit to her."
The angel of the LORD also said to her, "I will so greatly multiply your descendants that they cannot be numbered for multitude." (Genesis 16:9-10)
Abram was eighty-six when Ishmael was born to him (Genesis 16:16).
Fast forward fourteen years. Isaac was born to Abraham when he was one hundred (Genesis 21:5). Then Sarah told Abraham to drive Hagai and Ishmael away.
But Sarah saw the son of Hagar the Egyptian, whom she had borne to Abraham, playing with her son Isaac.
So she said to Abraham, "Cast out this slave woman with her son; for the son of this slave woman shall not be heir with my son Isaac." (Genesis 21:9-10)
Genesis does not tell us how old Isaac was. Probably he was still a baby. Then, what was wrong for an elder brother of fourteen years senior to play with a baby younger brother? Did Ishmael pose any threat to Isaac? The stated reason of Sarah was not very convincing. Ishmael should not be heir with Isaac. Did it warrant such a drastic action? What was the position of Abraham?
And the thing was very displeasing to Abraham on account of his son (Genesis 21:11).
Genesis is ambiguous here. What did "the thing" which was displeasing to Abraham refer to? That Ishmael played with Isaac? Or that Sarah told him to drive Hagai and Ishmael away? Who did "the son" refer to? Ishmael or Isaac? Read on.
But God said to Abraham, "Be not displeased because of the lad and because of your slave woman; whatever Sarah says to you, do as she tells you, for through Isaac shall your descendants be named." (Genesis 21:12)
Here, Genesis uses "the lad" to refer to Ishmael. Therefore, "the son" refers to Isaac. Furthermore, God has never intended Ishmael to be the son of Abraham. Ishmael was only the fruit of Sarah's design, not God's. God wants the chosen descendants to come from Sarah, not Hagai. The epistle to Galatians makes use of the contrast between Sarah and Hagai, a free woman and a slave to illustrates two covenants --- a covenant of promise and a covenant of law (Galatians 4:24). But it is a bit puzzling for the Galatians not to have mentioned Sarah by name! Enough digression! God made it clear to Abraham His intention to choose Isaac. God also told Abraham to follow Sarah's instruction to drive away Hagai and Ishmael. As for Ishmael, God would treat him generously because he was also the offspring of Abraham.
And I will make a nation of the son of the slave woman also, because he is your offspring (Genesis 21:13).
God kept His promise. When Hagai and Ishmael was desperate, God intervened and saved them.
And God was with the lad, and he grew up; he lived in the wilderness, and became an expert with the bow (Genesis 21:20).
God was and is with the Arabians.
Genesis 21 finishes with another etymology story of Beersheba. Abraham and Abimelech swore at that place.
Therefore that place was called Beer-sheba; because there both of them swore an oath (Genesis 21:31). 

עַל-כֵּן קָרָא לַמָּקוֹם הַהוּא--בְּאֵר שָׁבַע כִּי שָׁם נִשְׁבְּעוּ שְׁנֵיהֶם

Dear Lord, You call us to freedom from the bondage of sins. In freedom we walk. I pray for my mother. May she be redeemed from alcoholism. Amen.