Banishment of Hagar and Yishmael

Introduction

Innocuous Laughter?

Chapter 21 opens with a description of the birth of Yitzchak and the celebration to mark his weaning.  This happy scene is immediately spoiled when Sarah sees Yishmael "מְצַחֵק" (lit. laughing) and commands Avraham to banish and disinherit his son:

EN/HEע/E
(ט) וַתֵּרֶא שָׂרָה אֶת בֶּן הָגָר הַמִּצְרִית אֲשֶׁר יָלְדָה לְאַבְרָהָם מְצַחֵק. (י) וַתֹּאמֶר לְאַבְרָהָם גָּרֵשׁ הָאָמָה הַזֹּאת וְאֶת בְּנָהּ כִּי לֹא יִירַשׁ בֶּן הָאָמָה הַזֹּאת עִם בְּנִי עִם יִצְחָק.

What is the nature of Yishmael's "צחוק" and why does it bother Sarah?  Does it refer to innocent laughter and play or degrading mockery?  Or, perhaps, is it a euphemism for more heinous deeds?  If it was only innocent child's play, is it possible that the righteous Sarah would be ready to expel a son who had done no wrong?  On the other hand, is it conceivable that a son brought up in Avraham's household would have committed crimes so terrible that he deserved expulsion?

Hashem's reaction

The ambiguity of the term "מְצַחֵק" notwithstanding, Sarah's demand to banish Yishmael seems unduly harsh, and even Avraham at first appears disinclined to heed her words ("וַיֵּרַע הַדָּבָר מְאֹד בְּעֵינֵי אַבְרָהָם עַל אוֹדֹת בְּנוֹ").  A reader, though, who might have expected Hashem to intervene and reprimand Sarah, is surprised to learn that Hashem does the exact opposite:

EN/HEע/E
(יב) וַיֹּאמֶר אֱלֹהִים אֶל אַבְרָהָם אַל יֵרַע בְּעֵינֶיךָ עַל הַנַּעַר וְעַל אֲמָתֶךָ כֹּל אֲשֶׁר תֹּאמַר אֵלֶיךָ שָׂרָה שְׁמַע בְּקֹלָהּ כִּי בְיִצְחָק יִקָּרֵא לְךָ זָרַע.  

Hashem apparently finds no fault in Sarah, and He even directs Avraham to abide by her instructions.  This Divine endorsement suggests that more is going on in this story than meets the eye and that a re-evaluation of the actions of both Yishmael and Sarah may be necessary.

Other Questions

Other aspects of the treatment of Hagar and Yishmael are also troubling:

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