Erlkönig is not a children's poem. In the poem, a boy is assaulted and killed by a supernatural specter, while his father cannot even perceive the threat and is thus unable to defend him. That would be quite unsettling for children. Also the poem is mostly dialog, and the son, the father, and the eponymous Erlkönig speak in turns, with no indicator whose turn it is. I don't think many children would understand that.
I learned this in school (precisely because it was not considered a children's poem, but an example of great literary achievement that we should aspire to) 40 years ago; back then the naive interpretation was that the son fell sick while traveling with his father and suffered from delirium and hallucinations. The father was comforting his son, while trying to get him home for rest and medical care, but the son dies before they arrive.
Other interpretations focus more on the different perspectives of children and adults. The son is more susceptible to a more animistic world view; nature is alive and conscious, and speaks to him in voices both tempting and threatening. The rational father only hears the wind and the weather, and thus cannot understand what frightens his son that much.
Even other interpretations are build on the most unsettling lines from the poem, "Mein Sohn mich reizt deine schöne Gestalt // und bist du nicht willig, so brauch ich Gewalt" ("I love thee, I'm charm'd by thy beauty, dear boy! And if thou'rt unwilling, then force I'll employ", which is definitively not something you would write in a children's poem ). There are three speakers (father, son, Erl King), but only two persons present (father and son), and some people take this as a sign of the double nature of the father, as both the protective adult and the pedophile threat (who, it is implied, might have killed his own son).
You do not have to buy into any of these interpretations, but the fact that they are supported by the text means that this is not a naive children's rhyme, but an abyss that gazes also; whatever fear you bring with you will be reflected back upon you by the lines of the poem, and that is the reason why it is famous.