My gelding is not a rig however he will act like a stallion anywhere near mares. He won't try and cover them but he will fight with the other boys for the mares. Some geldings are just like that it seems.
I keep him with other geldings now well out of the way of other mares, I don't think this behaviour can be corrected, certainly not by a novice owner (me included in that).
Hope you find a solution that works for you