Then what prompted them to go to Utah?
They went to Ohio, then Missouri, then back to Illinois, and then when JS got shot, they split up into the Smith family Company (called Reorganized LDS) and the Brigham Young Brigade (who maintained the original name) and got out of Dodge and headed for the wilds of Utah to get away from all the people that they had hacked off.
The Smith family headed to Independence, Missouri and many different offshoots went their separate ways including many of the folks back East, in Wisconsin, Kentucky, and Texas.
Utah was pretty wild and bereft of law enforcement; it enabled Brigham Young to establish himself as ruler of essentially a principality, more or less outside the rule of law. There are many benefits that come with becoming a religious despot including the possession of as many young girls as it takes to satisfy one’s whim.