Joel, you say that exceptions make learning languages exceptionally tedious. (Like your play on words, btw.) But just about all languages have exceptions to rules and that is half the fun in learning them. What's the alternative? A contrived, artificial language like (I believe) Esperanto. How boring!
In 85% of cases, after the noun.
In front of an adjective, the indefinite article "des" becomes "de".
If you see "des vrais enfants" in a sentence, it means that "des" is not the indefinite article but the contracted definite article [de+les] = des.
For instance: il parle des vrais enfants = he is speaking of the real children (parler de = to speak of/about)
Would "these are truly children!" be closer to the meaning than the answer given?