Maybe I'm wrong but wasn't there effectively a Christian civil war when Constantine dangled power before the Christians?
Not exactly.
Constantine did not himself convert and get baptized until he was on his death bed. He was more friendly to Christians than most* previous emperors, but still honored Sol Invictus and traditional Roman Pagan gods during his reign as well. It is not really clear whether making Sunday a Day of Rest was primarily meant to honor Jesus or his Sun God more. Many worshipers of Sol Invictus since the time of Heliogabalus had actually considered Jesus to be one of many manifestations of Sol Invictus, but of course Christians considered that blasphemy.
(*Prior to Constantine a few emperors persecuted Christians severely, but most were indifferent and preferred to let local governors do whatever they thought best to stop potential riots. There were decades when it was safe to be Christian interrupted occasionally by a few years when it was dangerous. The worst persecutions were of course under Diocletian, who voluntarily retired and was still alive and planting cabbages during Constantine's reign. Diocletian was partially motivated by paranoia around how Christians were so over represented in secretarial roles in government bureaucracies, as they had much higher literacy rates than normal and were a quickly growing demographic due to their strong opposition to abortion/infanticide/birth control. Constantine himself was not the first emperor to have Christians friends and advisors, or even to attend church services. Some claimed Phillip the Arab himself became a Christian, but there is no evidence he was ever baptized or took communion. He did ask for the Eucharist at Easter one year, but was denied and told to sit with the penitents. At that time the vast majority of Christians believed that serving in the military or government in any role that involves either personally killing or ordering anyone else to kill anyone was completely incompatible with the faith. Some said soldiers could never be forgiven, while most merely required at least one full year of penitence after leaving the job before one could be allowed to take communion. Phillip the Arab fought wars and presided over the secular games at the 1000 year anniversary of the founding of Rome, an event marked by more gladiatorial combat than ever before or since.)
Constantine's Christian advisors were mostly Arians, not Trinitarians. When Constantine called the Council of Nicea, he probably wanted Arianism to be declared orthodox. He cared more about unity than any actual doctrines though. His ideal was to have one religion backing one emperor. He never named Christianity a state religion though, but had an edict of toleration for all religions. It was his son Theodosius who first tried to make Christianity a state religion and refused to punish those who destroyed pagan temples.
Constantine never dictated any doctrine, but he did give gifts to the Christians he liked best. Many churches had property stolen under his predecessors. He not only gave back plots of land but built basilicas on them, so the growing church had more impressive places to meet than private homes. His most extravagant gifts were reserved for those who supported him politically, or at least refrained from speaking out against his many sins.
Constantine got somewhat involved in the controversy around the Traditores, those Christians who had recanted their faith and collaborated with prior persecutions, handing over bibles to be burned and naming names of other church members to be martyred. Traditores were disproportionately from rich influential families (whose support Constantine needed), and were over represented among the (literate, well educated) priests and bishops instead of the laypeople. They were not popular among the christian laity. However, due to the issues around knowing whether baptisms were still valid if performed by an unworthy priest, and a lack of records to let people know who was baptized by whom, a synod of clerics in North Africa ruled that Traditores should be not only forgiven but fully reinstated into their prior offices of trust. When people protested and tried to call a new council for the whole church to decide what to do about the issue, Constantine prevented that. He also gave a lot of basilicas to churches led by Traditores.
This led to a schism where almost half of the church became Dontanists, who had basically identical doctrines but a separate hierarchy that was purged of Traditores in any ordained positions. (Dontantists were usually quite willing to accept Traditores who agreed to be laicized and did not try to exercise any authority over the community they previously betrayed.) Eventually the Dontanist and Catholic doctrines started to diverge, mostly because the Catholics became more friendly to state power while Dontantists continued to argue that Rome was the Whore of Babylon and the Emperor (whoever it happened to at the time) was the Antichrist. Some more radical offshoots were said to crave martyrdom so much that they would raid caravans and then turn over their weapons, begging their victims to kill them for their faith.
Augustine in his early years as a Christian wrote against the use of force to compel conversions, but later he saw that it actually seemed to work pretty well in suppressing Dontantists and so endorsed having the state torture and kill all such schismatics. There are correspondences between him and a Dontantist who argued for the early Christian pacifist position, in which Augustine insisted that they cannot claim a moral high ground because he chose to assume that they would certainly be the ones advocating violence against him if they were in a strong enough position to do so.
Of all the Emperors, the one who seemed to understand Christ's teachings best was Julian the Apostate, the first and only emperor to be raised as a Christian but then choose to return to Paganism. He seems to have been motivated in a large part by disgust at how hypocritical so many professed Christians were. He reversed edicts by predecessors like Theodosius and issued a new edict of toleration for all faiths. He returned some property to pagan priests that had been stolen by his predecessors to give to Christians. He refused to give Christians any positions of power in the military or civil government, citing scripture and early church fathers to argue that such roles were incompatible with their faith. He also forbid Christians from teaching the works of Homer or Hesiod (which were the core of standard curriculum for any respectable education), because he was offended by how they tended to teach that those works were allegories about the christian god instead of being obviously polytheistic texts. He had no problem with Christian schools and tutors instead using the Hebrew scriptures, the Septuagint, or really any text that did not invoke the Olympian gods though. He never seriously persecuted any Christians, but remained friendly towards those who did not seek political power while mercilessly mocking Christian hypocrites.