"Is koningin Máxima de moeder of vrouw van de koning?"
Translation:Is queen Máxima the mother or wife of the king?
We don't. After the queen steps down she is again a princess and assume everyone knows she was once queen. We don't have a term for the dowager queen either. She would probably become a princess again although I am not sure because we haven't had that situation in the last century. If you want a literal translation it would be something like de moeder van de koning/koninging depending on whether her son or daughter succeeded her.
HRH Beatrix will become a Queen again when she dies. To the best of my knowledge, she is HRH Princess Beatrix of the Netherlands etc. According to the precedent set by her mother and grandmother, Princess Beatrix will be buried as Queen Beatrix of the Netherlands
Why is the translation not "Is Queen Maxima the mother or the wife of the king?" it does not sound like a good English sentence
I don't think it's necessary to repeat the article in English (native English here), any more than it is in Dutch. You can if you want to, so I'm not sure it should be marked wrong, but it doesn't add anything to the meaning, and certainly doesn't improve the elegance of the sentence (in my opinion).