So the genitive plural of "dziecko" is "dzieci", just like the nominative plural?
Gen of dziecko is 'dziecka'.
L (o) dziecku
Yes, the genitive of "dzieci" (plural) is he same as the nominative: "dzieci" (see: https://en.wiktionary.org/wiki/dziecko).
to my ears, it sounds as if the children were an object, but I get it, different language - different mind