Clearly the issues that you are describing are beyond the normal scope of an average 3 year old. I don't feel comfortable expressing my thoughts on why she may be acting this way without observing the family in question. How I would view this little girl is that she is a child who is struggling and is most likely reacting to something in her environment. Most likely an adult should be held responsible. A child at that age is not to be blamed fully. This is my opinion, which is based on experience and knowledge.
It is important to view this situation with different eyes. Here are some suggestions:
- Separate the child from the behavior. Instead of viewing her as the violent child, view her simply as a child. A child who is acting in ways that you deem to be aggressive or violent. The former view attaches a heavy label on to this child, the latter view does not attach any of our own judgments of the child.
- Her behavior is reflective of her trying to meet her needs, just like adults. It is merely that we as adults already have an idea of what is acceptable measures of meeting our needs, she is still learning these social norms. Since she does not lack the inhibition that adults have, she acts in ways many adults only dream of acting.
I realize that there are certain behaviors that you are describing that we as adults in this society deem inappropriate and we would actively seek to modify while teaching her effective behaviors, labeling her the violent kid only pits her in a role she is far too young to handle.