4th Century Romans- Question: Soldiers And Standards Reverse

Two standards came first. Shortly before Constantine I died, the weight of coins was reduced and the second standard disappeared. All two standard coins issued by an Augustus belong to Constantine I because the change occurred while the sons were still just Caesars. Constantine I issued some coins with one standard but when he died Constantine II started issuing one standard coins using the title Augustus (AVG on obverse). These can be confusing. All the coins of Constans and Constantius II as Augustus will have just one standard. There will be coins with part legends that are missing name portions so you can't tell which boy it belonged to but any coin with two standards AND the title AVG on the obverse is dad's.

Seems to me that I heard somewhere (unfortunately I can't remember where at the moment) that the 2 standards reverse was issued during the time earlier in Constantine's reign when the Roman Empire was divided into 2 halves - the East and the West - and that the 1 standard reverse was issued after he had more or less united the 2 halves once again into a single empire - the last time the roman empire was one unified whole. Is this true or am I just blowing smoke here? Any ideas?