Yeah unfortunately that is not actually the way the law is written Bernie. Wish it was.
Short version, the president gets to deploy the military where ever he wishes (outside the US, posse comitatus etc). That includes invading a sovereign nation or raining missiles down on one.
Only congress has the power to declare a war, but the Potus gets to defacto kick off the war and then dare congress not to back him.
After it was either 60 or 90 days, I forget, congress gets to "review" the decision, the problem is they have no power other than financial if they wish to stop the war. So the only thing they can do is turn off the finances to the military, and wait for the money to run out - which is generally up to a year. They have no way of forcing the president to desist other than impeachment or cutting off the funds.
They can pass a motion, or even legislation, which the Prez can then veto, pointless. If they can muster the 2/3rds of congress they can remove him via impeachment.
Edit, spelling correction and to note that I can pull out the full details if needed - was discussed heavily on reddit a while ago