Matthew Poole and continuators on Genesis 21:10

10 Wherefore she said unto Abraham , cast out this bond-woman and her son, for the son of this bond-woman shall not be heir with my son, even with Isaac.

Being enraged by this fact and perceiving it was but a beginning and earnest of greater evil designed by him against her beloved Isaac; being also guided by the wise counsel and providence of God, as appears from ver. 12.

Though the fact was done by Ismael, yet Sarah plainly saw, that this and other like carriages were from his Mothers instigation and encouragement, who being of an imperious and petulant disposition, as appears from Gen. 16. 4, 9. in all probability comforted her self and animated her Son, by that right he had to his Fathers inheritance as he was his first-born, as may be gathered both from the custom of Women in such cases, and from the last words of this verse. Besides if the Mother had been continued, she would easily have prevailed with Abraham to fetch the Child back again.

Marginal references: Gal. 4. 30.