First, I am not speaking of the 'right of nations', even if there is such a thing. I'm speaking the right, within the US sovereign nation, of executive authority to act on behalf of the country in particular ways and circumstances. Some other nation may also have war-making powers granted to their special offices, be they democratic or not.
Second, as a general proposition it is my view that there is not a universal right of nation-states or nation state actions BEYOND that of which granted to each of us as individuals. As individuals we have a right to defend our security, our property, to obtain justice when defrauded or attacked. The actions of the nation state on their behalf is sum of those individual rights. The moral "rightness" of their acts should be measured against the same individual rights we believe it. Nation states that do not act on behalf of the individual rights of their citizens, but to (for example) build an empire don't have a right to make war.
Third, the primary or exclusive of our nation state is to protect the people and their liberty. It is NOT to protect the another people or their liberty. And as the world is a lawless place which does not play by our rules (so-called international laws to the contrary) other means must be employed beyond that of policeman and courts. Sometimes that includes military force.
An "act of war" has no inherent meaning beyond that of which is customarily agreed to between nations. Anything can be an act of war in the minds of the rulers of a nation, but the legitimacy of an act of war is purely dependent upon its purpose in protecting the individual liberty and safety of those doing so.
So while an act of war may be limited to military actions (and generally is), typically actions that don't include violence are not. None the less, an act of war is not a discrete thing with a universal definition.