"The queen gave her tasks to her son."
Translation:De koningin gaf haar taken aan haar zoon.
"De koningin heeft haar taken aan haar zoon gegeven" any reason why it would be wrong?
But it was stated before that the difference between present perfect and simple past is mostly one of style in Dutch, not of meaning.
Waarom kan ik niet zeg "de koningin gaf aan haar zoon haar taken"? Ik dacht dat dit ook juist zou zijn.
haar zoon is the Indirect Object in this sentence, the Direct Object being haar taken.
When the IO precedes de DO, aan is not used. Aan is only required when the IO comes after the DO.
De koningin gaf haar zoon haar taken.
De koningin gaf haar taken aan haar zoon.
Compare it to the English counterparts:
The queen gave her son her tasks.
The queen gave her tasks to her son.
But never<h1>The queen gave 'to' her son her tasks. (Ungrammatical!)</h1>
Here we have pretty much the same situation as in Dutch: to is only required when the IO (her son) comes after the DO (her tasks).
Hope this helps.
If used as a preposition, door cannot be used in this context, it would mean by.
Now, if it had been part of the separable verb doorgeven (pass on, pass down), then the sentence would need to be altered:
De koningin gaf haar taken door aan haar zoon.
The detachable part of separable verbs (here doorgeven) is placed after the Direct Object but before the Indirect Object.
Anyway, keep in mind that you'd be changing the verb, and thus the translation is not exactly the same as the original.