A Commentary, Critical, Practical, and Explanatory on the Old and New Testaments, by Robert Jamieson, A.R. Fausset and David Brown  at sacred-texts.com
gen 21:1BIRTH OF ISAAC. (Gen 21:1-13)
the Lord visited Sarah--The language of the historian seems designedly chosen to magnify the power of God as well as His faithfulness to His promise. It was God's grace that brought about that event, as well as the raising of spiritual children to Abraham, of which the birth of this son was typical [CALVIN].
gen 21:3Abraham called the name of his son . . . Isaac . . . and circumcised--God was acknowledged in the name which, by divine command, was given for a memorial (compare Gen 17:19), and also in the dedication of the child by administering the seal of the covenant (compare Gen 17:10-12).
gen 21:8the child grew, and was weaned--children are suckled longer in the East than in the Occident--boys usually for two or three years.
Abraham made a great feast, &c.--In Eastern countries this is always a season of domestic festivity, and the newly weaned child is formally brought, in presence of the assembled relatives and friends, to partake of some simple viands. Isaac, attired in the symbolic robe, the badge of birthright, was then admitted heir of the tribe [ROSENMULLER].
gen 21:9Sarah saw the son of Hagar . . . mocking--Ishmael was aware of the great change in his prospects, and under the impulse of irritated or resentful feelings, in which he was probably joined by his mother, treated the young heir with derision and probably some violence (Gal 4:29).
gen 21:10Wherefore she said unto Abraham, Cast out this bondwoman--Nothing but the expulsion of both could now preserve harmony in the household. Abraham's perplexity was relieved by an announcement of the divine will, which in everything, however painful to flesh and blood, all who fear God and are walking in His ways will, like him, promptly obey. This story, as the apostle tells us, in "an allegory" [Gal 4:24], and the "persecution" by the son of the Egyptian was the commencement of the four hundred years' affliction of Abraham's seed by the Egyptians.
gen 21:12in all that Sarah hath said--it is called the Scripture (Gal 4:30).
gen 21:13also of the son of the bondwoman will I make a nation--Thus Providence overruled a family brawl to give rise to two great and extraordinary peoples.
gen 21:14EXPULSION OF ISHMAEL. (Gen 21:14-21)
Abraham rose up early, &c.--early, that the wanderers might reach an asylum before noon. Bread includes all sorts of victuals--bottle, a leathern vessel, formed of the entire skin of a lamb or kid sewed up, with the legs for handles, usually carried over the shoulder. Ishmael was a lad of seventeen years, and it is quite customary for Arab chiefs to send out their sons at such an age to do for themselves: often with nothing but a few days' provisions in a bag.
wandered in the wilderness of Beer-sheba--in the southern border of Palestine, but out of the common direction, a wide extending desert, where they lost their way.
gen 21:15the water was spent, &c.--Ishmael sank exhausted from fatigue and thirst--his mother laid his head under one of the bushes to smell the damp while she herself, unable to witness his distress, sat down at a little distance in hopeless sorrow.
gen 21:19God opened her eyes--Had she forgotten the promise (Gen 16:11)? Whether she looked to God or not, He regarded her and directed her to a fountain close beside her, but probably hid amid brushwood, by the waters of which her almost expiring son was revived.
gen 21:20God was with the lad, &c.--Paran (that is, Arabia), where his posterity has ever dwelt (compare Gen 16:12; also Isa 48:19; Pe1 1:25).
his mother took him a wife--On a father's death, the mother looks out for a wife for her son, however young; and as Ishmael was now virtually deprived of his father, his mother set about forming a marriage connection for him, it would seem, among her relatives.
gen 21:22COVENANT. (Gen 21:22-34)
Abimelech and Phichol--Here a proof of the promise (Gen 12:2) being fulfilled, in a native prince wishing to form a solemn league with Abraham. The proposal was reasonable, and agreed to [Gen 21:24].
gen 21:25And Abraham reproved Abimelech because of a well--Wells were of great importance to a pastoral chief and on the successful operation of sinking a new one, the owner was solemnly informed in person. If, however, they were allowed to get out of repair, the restorer acquired a right to them. In unoccupied lands the possession of wells gave a right of property in the land, and dread of this had caused the offense for which Abraham reproved Abimelech. Some describe four, others five, wells in Beer-sheba.
gen 21:33Abraham planted a grove--Hebrew, "of tamarisks," in which sacrificial worship was offered, as in a roofless temple.
gen 21:34Abraham sojourned in the Philistines' land--a picture of pastoral and an emblem of Christian life.