What you have just described is radical Islam.
Andy, there is no such thing (and never has been) as “radical Islam.” One would have to suppose there was an opposite site, a non-radical side to Islam - there is not. There is only the ‘fundamental’ that is the original Islam. It is unchanged since the Founder brought it forth; further it cannot change as the Founder said: Death to all those who make the attempt.
What you mistake for a ‘peaceful’ Islam is all the time after it was defeated and driven into ‘hiding’ for the past centuries. It is a tactic used to low the kafir into believing Islam is harmless. When the time is right they attack - after the end of the cold war, Islam perceived the west weak and began to ramp up into what we experience today. Do not be deceived by the incessant taqyyia (permitted lying in defense of Islam) put forth by CAIR and the complicit media.