I am having trouble understanding exactly what malice is and how it is different from aggression? In social psychology, aggression (which is contrasted with accidental harm) is defined as intentional act to cause harm, whether it is as means to an achieve some other goal (instrumental aggression) or as an end in itself (hostile/impulse aggression). On the other hand, malice is also defined as intentional or purposeful desire to do harm. So keeping this in mind, would it be appropriate to think that every act of aggression, whether instrumental or impulse, is essentially malicious?
malice: The intention or desire to do evil; ill will.
aggression: Hostile or violent behavior or attitudes toward another; readiness to attack or confront.
You should probably consult a lawyer, :-) but malice involves intent or desire, whereas aggression goes beyond malice into the realm of action or readiness for action.
In a way, you answered your own question by characterizing, in social psychological terms, aggression as an act and malice as a desire.
Addendum: Given the definitions of aggression and malice you provided, you asked if it would be appropriate to think that every act of aggression, whether instrumental or impulse, is essentially malicious? I would say no. Take corporal punishment, for example, which could involve an intentional act to cause harm with no intentional or purposeful desire to do harm. As many an "old-school" parent has said, "This will hurt me a lot more than it hurts you."