rein him in + rein her in + rein them in = total 60,720 hits
reign him in + reign her in + reign them in = total 26,720 hits
free rein = 769,000
free reign = 1,010,000 hits
Traditionalists say both expressions call for rein. To rein someone in is a reference to a horse's reins and means to get someone under control. Conversely, to give free rein means to let someone or something run wild. (I've actually done this on a horse = let go of the reins, yelled "ha!," and seen where I ended up [I was young].)
But you could, if you wanted to, make a case for free reign, since reign, like rein, refers to control or power. In fact, some sources sanction free reign, sort of.
But think twice before you include the G -- a lot of us "we were taught differently" types will assume your spelling is out of ignorance and not conscious choice.