"She wants to send a letter to her parents."
Translation:Ŝi volas sendi leteron al siaj gepatroj.
It was accepted for me with a note to "watch the accents," meaning Duo thinks its a misspelling instead of an alternate translation. However, as has been pointed out, from English either "ŝiaj" or "siaj" should be accepted. Without context, one cannot tell whose parents are being referred to, i.e. the subject's parents (her own) or the parents of a female friend (her).
It is correct, technically; but it places the emphasis on the letter itself, which is what makes it nonstandard. You might hear it in a poem, or if there's a particular reason to emphasize that it's a letter that she wants to send (and not an anniversary gift, for example).
The flexibility of the word order is an oversold feature of Esperanto. Think of it as speaking like Yoda; people will most likely understand you, but you'll definitely get some looks.