Here is the second in my "WILD SPECULATION" series, the last one being:
http://www.jehovahs-witness.com/10/49483/1.ashx Did the Prophet Daniel Commit SUICIDE? (based on evidence of his increasingly desperate chronology adjustments)
We already know that Abraham's household was abusive (allegedly). If you look deep enough, almost every story could be a story of spousal abuse or child abuse.
Example 1: When Sarah couldn't get pregnant she offers her own servant Hagar, but when Hagar gets pregnant, Sarah "begins to despise her" (Gen 16:4), claims Hagar despises her, and basically can't handle the tensions of this new situation. Abraham lets Sarah know Hagar is at Sarah's "disposal" so she throws the pregnant women out to fend for herself in the "wilderness." Sarah "began to humiliate her so that she ran away from her" (v.6) But Hagar ends up turning around and coming back to the abusive household. (Abraham at 99 got circumcised as part of a deal with God to get more children. In fact, Ishmael at 13 years old had to get his foreskin cut off, and so did (v.27) "all the men of his household, anyone born in the house and anyone purchased with money from a foreigner.")
Example 2: Genesis 19, throws in a story about Abraham's nephew (son of his brother) Lot. We find Lot protecting a couple of strangers from a "mob" ranging from "boys to old men" who kept yelling for Lot to "bring them out to us that we may have sex with them." (v.5) Lot says: "Do not act badly. Please, I have two virgin daughters, please have sex with them instead. Please let me bring my girls out, and then you can do whatever you please with them." By the end of chapter 19 those two daughters are getting Lot drunk and having sex with him. They both got pregnant.
Example 3: Chapter 20. Abraham while going through King Abimelech's territory is afraid they might kill him because of his wife. Gen 20:11 makes it sound as if Abraham had some unfounded paranoia. Anyway Abraham repeatedly claimed that Sarah was only his sister (v.2), so that the King sent and took Sarah. According to v.13, Abraham said Sarah was supposed to play along and say Abraham was her brother. It all worked out just fine, however when the King dreamed that he she was owned by another, and he has to give her back or else "know that you will positively die, you and all who are yours." Rich Abraham somehow leveraged this situation so that Abimelech offered him land, sheep, cattle, men slaves, and women slaves. Sarah got 1,000 silver pieces.
Example 4: Isaac's name means "laughter" but it can also mean "make fun of (derisive laughter)" or even "make sexual foreplay (secret laughter)." The name is onomatopoeic
But my point in this example is this: Ishmael was last identified at 13 years old, but might be as old as 18 or 19 when Isaac gets weaned at about age 5. Genesis 21:9 is usually translated along the lines of "And Sarah saw the son of Hagar the Egyptian, which she had born unto Abraham, mocking.
The Septuagint (LXX) change to wording to show that the tsachaq was definitely directed specifically against Isaac and the Targums and other commentaries dance around the idea that it was something more offensive. Even the Aid book says on p. 841 "Some translations say that Ishmael was only 'playing' with Isaac...However tsa-hhaq' can also have an offensive connotation."
I'm conjecturing, as others have, that the connotation is that Ishmael abused Isaac. In Galatians 4:29, Paul thought of whatever it was as representing "abuse" or "persecution" (NWT).
Example 5: Terrorizing Isaac by tying him to an altar of sacrifice and pulling a knife on him has already been commented on enough.