..not quite.
Ismael was NOT rejected by his father .. nor his mother.
Abraham, peace be with him, thought it best to separate his wives, because they didn't get on.
It all started when the wife who thought she couldn't have a child, did have one. Isaac.
Gen 21:14 So Abraham got up early in the morning and took bread and a skin of water, and gave
them to Hagar, putting
them on her shoulder, and
gave her the boy, and sent her away. And she departed and wandered about in the wilderness of Beersheba.
15 When the water in the skin was used up, she left the boy under one of the bushes. 16 Then she went and sat down opposite him, about a bowshot away, for she said, “May I not see the boy die!” And she sat opposite him, and (
A)raised her voice and wept.
Yes, Abraham who was very rich in camels cattle, sheep, servant etc, as a loving father, sent his wife and son with water and bread. No camels, no money no hope.
I don’t know what you define as rejected, but this comes pretty close IMV.