I notice that "my daughters are your daughters" is not accepted - is the implication that these might be "my" girls in some other sense ?
good question. in other contexts daughter is a perfectly acceptable translation. I reported it, but would like to hear from native speakers what they think.
Because ילדותי and ילדותךָ would mean "my girl" and "your girl" (singular). Check out the tips and notes for this lesson, they give a helpful paradigm.
"my girls are your girls", the "correct" translation, is quite different in meaning from "my daughters are your daughters". The former may be construed as a transfer of property, while the latter may reflect joint parenthood.
In relation to Dov's remark,
Would ילדותיי הן הילדות שלך tend to serve more as an indicator of property, vs. Duo's sentence, as more of an indicator of joint parenthood ?
Should not be: יַלְדוֹתַי הן יַלְדוֹתֶיךָ? Isn't the second yud only possible in יַלְדוֹתַיִיךְ (your f. sg. girls)?