Is it "jedno" (neuter) rather than "jedna" (feminine) because jedno refers to the singular "dítě " (neuter) even though dětí is feminine?
I'd say so.
why isn't the accepted? we can also say one of the children is hers even when meaning these while standing close the children
You can say many things, when meaning something, but not all of them will be translated the same way.
Please try to distinguish between this and the/that.