וַיִּקְרָ֨א אַבְרָהָ֜ם אֶֽת־שֶׁם־בְּנ֧וֹ הַנּֽוֹלַד־ל֛וֹ אֲשֶׁר־יָלְדָה־לּ֥וֹ שָׂרָ֖ה יִצְחָֽק" 3
וַתֹּ֣אמֶר שָׂרָ֔ה צְחֹ֕ק עָ֥שָׂה לִ֖י אֱלֹהִ֑ים כָּל־הַשֹּׁמֵ֖עַ יִֽצְחַק־לִֽי" 6
"And Abraham called the name of his son that Sarah bore him, Isaac... And Sarah said, 'God made me laugh; all that hear will laugh (with) me.'" (That's my rough understanding of the Hebrew but I'm a noob at it so I may have gotten some things wrong.) What I'm asking about is the connotation of "יִֽצְחַק" and "צְחֹ֕ק" in these verses.
I'm using Strong's Hebrew lexicon and it states:
H6711 צחק צָּחַק tsâchaq tsaw-khak‘ A primitive root; to laugh outright (in merriment or scorn); by implication to sport: - laugh, mock, play, make sport.
Also for Isaac's name (which is I think the Qal Imperfect Singular 3rd person?) it says:
H3327 יצחק יִצחָק yitschâq yits-khawk‘ From 6711 laughter (that is, mockery); Jitschak (or Isaac), son of Abraham: - Isaac. Compare 3446
Both of these seem to imply that "צָּחַק" is being used in a connotation of mocking more than of innocent laughter. Is this correct? It doesn't seem to me like Sarah wants other people to join her in mocking in verse 6, but if she is, say, giving those who mocked her for being childless the proverbial taste of their own medicine, it seems to change the understanding of these verses and (at least) Sarah's understanding of Isaac's name.