It's weird how things start making sense and we do not even realize! Let's keep going, ludzie!
To be fair, I had to look up dzieckiem but I know what you mean (well, with other sentences).
Generally, Accusative is for the direct object, and Instrumental for using something as an instrument, for doing something 'with' something/someone, and sentences like here: "You are a child".
Why is the instrumental of dziecko not dzieckem? Just a weird declining case?