Just ask the dictionary:
Japanese to English dictionaries often tend to gloss over a lot of nuances, so it's good whenever possible to use a J-J dictionary. In English, this would read as "something for which you hold deep affection and treat as important." The examples refer to "my 'dear' son," for example, which matches the usage of your sentence. The example sentence in question would be "わたしのかわいい息子へ".
So as for whether it's a 'true' translation, which I assume you mean not to be in error, or else a literal translation, the answer is of course yes. Because the speaker cares deeply for this child he/she scolds him/her. Technically it COULD be that the speaker is just weird and especially enjoys scolding cute kids, but we have no context to suggest that the definition above is not the most likely one.
Definition 2 in that dictionary entry is the one that has the typical "cute" meaning that we tend to associate with the word