Yet Constantine remained an unbaptised non-christian until he accepted baptism by Semi-Arian Bishop Eusibius of Nicodemia.
As I understand it, he then banished all Nicene bishops/priests from Rome and brought back the previously banished Arian Bishops/Priests.
And finally committed his son Constantinus(?) to be a Arian-Christian emperor.
Obviously Constantine had regrets about the Nicene Creed which he in-part dictated and coerced through threat of banishment.
Yet Constantine remained an unbaptised non-christian until he accepted baptism by Semi-Arian Bishop Eusibius of Nicodemia.
First, catechumens, which Consantine was, were considered Christians. So to say he was unbaptized is correct. To say he was a non-Christian is not correct.
As I understand it, he then banished all Nicene bishops/priests from Rome and brought back the previously banished Arian Bishops/Priests.
Your understanding is not correct. Constantine presided at the Council of Nicea which condemned Arius. He did banish some bishops -- orthodox and Arians alike -- mainly because he was attempting to quell their constant bickering which he did not fully comprehend.
And finally committed his son Constantinus(?) to be a Arian-Christian emperor.
Constantine had three sons, all of whom inherited the empire from him. Two were more orthodox (Constantine II and Constans), one was more Arian (Constantius II).
This era of history is fascinating and complex. I suggest reading the following which, in my opinion, is the best modern biography of Constantine available:
Constantine and the Christian Empire by Charles Odahl.