Does God's sovereignty mean He approved of Abram having a child by the slave woman?
No. Although God sovereignly controls the flow of events, the biblical text shows God had nothing to say about Abram having a child by the slave woman. That plan came from Sarai and Abram, not from God, and Scripture calls it after the flesh, while Isaac is the son of promise.
Les explains that in this Genesis account, God is totally lacking from the conversation. God had only promised to make a nation from Abram, which required a son. Sarai proposed using her maid, and Abram listened to her voice. Les notes that God had not said a word, and the Hagar/Ishmael scenario is called after the flesh in Galatians. Isaac would be the son of the promise. Les acknowledges that sovereignly God was controlling the flow of events, but as far as the text is concerned, God had nothing to say about having a child by the slave woman. So sovereignty is not the same as approval; God did not endorse or command that act.
And Sarai said unto Abram, Behold now, the LORD hath restrained me from bearing: I pray thee, go in unto my maid; it may be that I may obtain children by her. And Abram hearkened to the voice of Sarai.
More Questions
Why did Sarai tell Abram to have a child with Hagar?
Sarai acknowledged that the Lord had restrained her from bearing, and she then initiated surrogate motherhood by asking Abram to go in to her maid Hagar to obtain children by her.