So to carry a 12GA or .223 Cal [5.56mm] in the car it must be modded to "become" a pistol and registered as such per MI. law.
There is a lot to get jammed up on here so study the law before you do anything. One user you can PM is lapeer20m if he doesn't mind / he carries a 12GA in this config.
If you don't want the hassles then just use transport mode This means stored in the trunk (or if no trunk, in a spot inaccessible to the occupants - meaning as far away from them as possible) in an "approved" container, unloaded etc... ,as you would with any long gun on range, hunting trips etc...
Hope this helps.