I read the commentaries but feel they do not convey the prophetic voice (decree) of Sarah. One must first ask why Sarah needs to say im bni “with my son,” then say im yitzchaq “with Isaac;” as Sarah has only one son!
See Rashi to 20.18 and 21.12.
Rashi to 20.18:
because of Sarah: Heb. עַל דְּבַר, lit., by the word of Sarah. Through the words of Sarah. — [from Gen. Rabbah 52:13] the wombs of Abimelech’s House were “closed up;”)
hearken to her voice: (to the voice of the holy spirit within her.) We learn from here that Abraham was inferior to Sarah in prophecy. — [from Exod. Rabbah 1:1, Tan. Shemoth 1]
Here is the way I read the passuk (21.10) to eliminate the superfluity – “shall not inherit with my son, with laughter (mockery)” –
with my son, etc.: From Sarah’s reply, “For the son of this handmaid shall not inherit with my son,” you learn that he would quarrel with Isaac regarding the inheritance and say,“ I am the firstborn and should take two portions,” and they would go out to the field, and he would take his bow and shoot arrows at him, as it is said (Prov. 26:18f.): “Like one who wearies himself shooting firebrands, etc. and says: Am I not joking?” –
Ishmael mocked the Covenant of Circumcision as it says,
“And Sarah saw the son of Hagar the Egyptian, whom she had borne to Abraham, making merry [mocking].”
making merry: Heb. מְצַחֵק. An expression of idolatry, as it is said (Exod. 32:6):“and they rose up to make merry” (לְצַחֵק) . Another explanation: An expression of illicit sexual relations, as it is said (below 39:17):“to mock (לְצַחֶק) me.” Another explanation: An expression of murder, as it is said (II Sam. 2:14):“Let the boys get up now and sport (וַיִשַׂחֲקוּ) before us, etc.” – [from Gen. Rabbah 53:11]
And some say,([in reference to 22.1])“ after the words of Ishmael,” who was boasting to Isaac that he was circumcised at the age of thirteen, and he did not protest. Isaac said to him,“ With one organ you intimidate me? If the Holy One, blessed be He, said to me, ‘Sacrifice yourself before Me,’ I would not hold back.” – Cf. Gen. Rabbah 55:4.
I read 22.1 as “after the words [of Sarah]” – גָּרֵשׁ הָאָמָה הַזֹּאת, וְאֶת-בְּנָהּ: כִּי לֹא יִירַשׁ בֶּן-הָאָמָה הַזֹּאת, עִם-בְּנִי עִם-יִצְחָק.
This phrase im Yitzchaq is a “double entendre;” as HaShem said, “I will establish My Covenant with Yitzchaq” and said, “for in Yitzchaq will be called your seed.” See Tehillim 2.4
King David in Tehillim 105.9 prophesied that Yitzchaq’s name would one day be changed to Yischaq. (See also Jeremiah 33.26 where it is also spelled Yischaq).
The Netsiv points out that one day HaShem will vindicate the Children of Israel turning the mockery into laughter of the mouth:
“Says Netsiv, David foretold through divine inspiration that some day, the patriarch would be renamed to indicate the full joy that would replace the mockery.” Rabbi Naftali Zvi Yehuda Berlin of Volozhin, Ha’amek Davar: Commentary on the Pentateuch, New York: Friedman.
Tehillim 126.2 “Then was our mouth filled with laughter שְׂחוֹק , And our tongue with singing; Then said they among the nations: ‘The L-RD hath done great things with these.’ “
Job 8.21 “Till He fill thy mouth with laughter, and thy lips with shouting. 22 They that hate thee shall be clothed with shame; and the tent of the wicked shall be no more.”
Tehillim 37.13 “The L-rd doth laugh at him; for He seeth that his day is coming.”
If one reads im Yitzchaq as a proper name then there is superfluity but if one reads it as a prophetic decree then there is no superfluity!
Yochanan Ezra ben Avraham