There are three "sons" mentioned in this chapter: Abraham's sons (Isaac & Ishmael) and Abimelech's son (unnamed). Were these 3 sons so different? Initially (and, by that, I mean "at birth" and "hypothetically"), perhaps, they all had similar potentials... but they were not in any way destined for the same fate. Perhaps the most noteworthy issue here is Abraham's handling of these three individuals. It is an interesting little study.
1. Isaac: Obviously, this was the promised son. He naturally received very special treatment. He was the son of Sarah (the wife of Abraham's youth). He was given by God as a miracle baby and was delivered with a guarantee: "Father of Millions," Wow! He brought great joy to the couple. His name meant "laughter" and he evidently produced a lot of it.
2. Ishmael: As a young teenager, this boy's behavior (or misbehavior) was an omen of things to come. It appears that at his half-brother's "weaning feast" Ishmael made a fool of himself by making fun of his little brother. His nonsense cost him (and his mom) his home. Perhaps it was inevitable, yet there it is. Then Sarah acted like the jealous-motherthat-she-was and lastly Abraham acted like a-broken-hearted-father/husband-in-a-verydysfunctional/blended/broken-family. Whatever the circumstances though, it is still a hard and harsh commentary: with God's permission and reassurance Abraham expelled Hagar and Ishmael. He sent them away with bread and water... in order to keep peace with his wife and to protect his favorite (or at least, favored) son. Good news (sort of): Ishmael was protected and blessed by God and became a success too (by God's grace, but not to God’s pleasure).
3. Abimelech, Jr.: This was not one of Abraham's sons. Abraham did actually have more sons later in life (see Genesis 25:1-6) after Sarah died, but Abraham wasn't related to this young man. So why bring him into the discussion at all? Well, I didn't bring him in, God did. In Genesis 21:22- 24 we have a record of Abraham making a covenant peace with Abimelech AND HIS SON. Wait! He just kicked his own son out of the house (well... tent) on his rump, now he makes a 3 generation agreement with Abimelech (including the son of that Philistine king). He gave Ishmael bread and water; he gives these dudes sheep and cattle!? Sorry, seems strange to me! The contrast is at least remarkable! Yet, God had a plan.
Well, whatever Abraham's faux pas and idiosyncrasies, he had one thing right: he knew who God was and he turned to Him in faith. If we place any value on Romans 10:13 kind of doctrine then we must conclude that Abraham (despite his flaws) was accepted of God... and, ultimately, that's what matters most.