"The young girl called for her dog."
Translation:Den lille pige kaldte på sin hund.
I think it should differentiate more clearly between young and little or small.
Perhaps you'll be comforted by the fact that a lot of danes actually say "hendes" or "hans" in situations where the correct word according to language lawyers is "sin" or "sit". The latter words are less ambiguous because they refer back to the subject of the sentence whereas "hendes" and "hans" can refer to different persons depending on context.
Den gamle dames hund var blevet væk. Den lille pige kaldte på hendes hund.
This example lends context to the sentence and makes it seemingly obvious that the little girl is not calling her own dog but rather the old womans dog. If you substitute "sin" for "hendes" there will be no doubt that the little girl is calling for her own dog.
I hope this helps dissolve your confusion.
Just to be clear: "Den lille pige kaldte på hendes hund" is a perfectly valid translation for "The young girl called for her dog" when you have no other context. This is because the English sentence is ambiguous. In Danish the words "sin" and "sit" remove that ambiguity. You cannot know whether to use "sin" or "hendes", so both should be accepted. However this sentence probably appears in a section about "sin" and "sit".