God in his grace came to Sarah, what He did we don’t know, but God kept his promise and the laughter Isaac was born. When Isaac was about 3 years old Sarah and Abraham could stop nursing him as a helpless child and start the teaching and demanding period. Today children are being nursed far too long; the children enter school not prepared for it.
Isaac was now at least 3 years old, probably 5 or 6, that made Ishmael about 19, 20 years old. Ishmael was grown up; he was old enough to know not to mock the 5/6 year old Isaac. The normal scenario would have been that Ishmael bothered Isaac, and Sarah talked to him and Ismael stopped doing it, but when he thought nobody saw him, he did it again.
Then Sarah talked to her maid Hagar, and she also talked to Ishmael, but in a respectful way, Ishmael was about 20 and Hagar knew that God had promised to make him a people. Ishmael also knew he was to become the father of a nation and I think that his high thoughts of himself made him treat Isaac as an inferior.
When the mocking didn’t stop Sarah went to Abraham asking him to send Hagar and her son away from them. This bothered Abraham and he didn’t know what to do, he loved his son Ishmael also. This was just a family matter, quite normal for a family to have some trouble like that, especially if you have two wives.
But God found it important enough to intervene; He spoke to Abraham and told him to listen to Sarah and do as she said. God was to look after both Isaac and Ishmael not because of them, but because of Abraham, God blessed the descendants of His prophet. Abraham was in the center, all around was a blessing for him. It is the same with you today, if you follow Jesus all people around you are blessed too, and they are a blessing to you, it is not because of them, but it is God’s relation to you through Jesus.