Constantine didn't convert the Roman Empire to Christianity, he established toleration for Christianity and initiated personal patronage of Christianity as well as generally favouring Christians.

Secondly, while religious violence is certainly not unknown in the ancient world, 'terrorism' is a product of modernity, which in my view cannot stably be talked about before the emergence of political violence and terrorist in the 19th century. It runs the risk of presentism and inaccurate anachronism to try to understand religious violence in Antiquity as 'terrorism'.

You're thinking of Edict of Milan in 313, which simply was meant to stop religious persecution in the Empire. The Edict specifically singles out Christianity, and was created primarily due to Christianity's influence on Constantine, but it was not only about Christianity and certainly did not "convert" the Roman Empire to Christianity, nor was Constantine a Christian at this point either. At this point Hellenistic religions continued to coexist with other religions including various forms of Christianity. The official religion of the Roman Empire was not Nicene Christianity until Theodosius I issued the Edict of Thessalonica in 380. At this point, Theodosius ended religious tolerance and began to persecute the Hellenistic religions and non-Orthodox Christian sects. Yes, there was violence, and Hellenistic temples were demolished. If you want to read further, I suggest you start with Dale T. Irvin and Scott W. Sunquist's History of the World Christian Movement, Volume 1