Not so, Yarden. I imagine someone who is forming a melded family and says to his new wife "my daughters are your daughters. now." Also someone who (like my parents, esp when angry) said "do you know what your daughters just did?"and the person answers (with or without snark, acc to the tone) "my daughters are your daughters.
The first Hebrew word you give, ילדותי with the single י would not be correct because “my girls” needs the double יי and in fact, in this Tips section, only the plural possessive of “my” had the double יי. As for the last word that Duolingo gives, they put the double יי there, and since they said in the Tips section that the double יי only goes with “my plural possessive”, it doesn’t seem to match the “your masculine singular” (yaldoteikha).