You might very well be overreacting. When horses are turned out together, then biting, nipping, kicking is quite natural to them, especially when their hierarchy has not yet been fully settled. This sometimes takes more time if the horses are stalled overnight and don't get the chance to live together in a herd environment 24/7. Don't cut your mare off from the company of other horses, they will sort everything out by themselves.
Of course, if the other horse is persistently and overly violent, inflicting serious injuries on your horse, etc., you might consider turning your mare out with some other horse.
I have come a long way, to surrender my shadow to the shadow of my horse.