Destructive childis quite serious. However, if the child enjoys breaking things, then he or she is destructive, perhaps even sadistic, cruel, or psychopathic. That type of behavior is usually a very bad sign.
On the other hand, if you want to say that the child has trouble sitting still, and he or she often breaks things (but is not mean, or doesn't intend to break things), then you could say the child is restless, clumsy, accident-prone, perhaps spoiled, not well-behaved, and can't keep his or her hands to him/herself.
Thanks owlman5 and Cambria. "destructive" sounds pretty strong to me too. "naughty" is still general. A "restless" child typically doesn't stay still but he might not like touching things and breaking them.
Unruly would certainly work. Wayward has literary and religious significance in English, and it would imply that the child has left home and gotten in serious trouble. If you are curious about this, look up the phrase wayward son. Poorly behaved and unable to keep his hands to himself both imply a child who gets into trouble but isn't mean-spirited.