Historians in more recent years are seriously questioning whether or not the Northern Kingdom of Israel, and the Southern Kingdom of Judah were ever really united, and if so, how senior a partner the tribe of Judah would have been in such an arrangement. The lands of Israel were always much richer than those of the dry hills of Judah, and Judah never attained the level of development that the Northern Kingdom did. As well, it is very likely that all of the so-called ten tribes were in fact Cannanites from the beginning, and such practices continued in the Northern Kingdom right up until its demise.
Rather, some consider the much of the Deuteronomic history of the Bible to have been written in the reign of the King Josiah for the explicit political purpose of uniting the peoples of these two lands once Assyria was out of the picture left open a window of opportunity.
All this is to say that the degree that Jeroboam rejected Jerusalem as a worship site is really open to question. It is just as possible that the Northern kingdom already had worship sites of their even before David and Solomon established themselves in Jerusalem.
In terms of the trio of Mohammed, Constantine, and Jeroboam, perhaps a better anology would be the even greater similarities between Moses, Mohammed, and Constantine. Muslims have always quite correctly pointed out that Mohammed style was very much in the likes of Moses, in that both brought God's law to God's people, and were very much involved in military conquest as the adequate means of doing so. While Constantine was never much of a religious personality, he too was very interested in a common spiritual belief unifying his empire into a cohesive political, military and social force.
Unlike either Moses or Mohammed, though, Constantine is not really responsible for any of the changess that Christianity brought to the Old Covenant religion. Gathering on the 'eight day' of the resurrection was an established practice of many of the early followers of the Way long before Constantine arrived on the scene. Nor did he really change any the laws of the Roman empire in any significant way according to Divine command. He was mainly a political and military character, and he left the decisions of a more spiritual nature in the hands of the Church.
As a final note, Zug-Zwang, with all your talk of Ishtar and Constantine changing the site of worship from Jerusalem to Rome( actually he changed the heqdquarters of his empire from Rome to Constantine), you are painting into a corner occupied by the superstitious and the uninformed.