I generally breed or own aqha's or apha's but have owned a variety, and I will NEVER keep a stallion that is aggressive towards humans.
These two being aggressive towards one another is no surprise - they are stallions, and when mares are present or nearby, aggressive behavior shouldn't be a shock. Though your stallions do sound quite excessive. (and both in the ring at the same time is a mistake if they are that unmanageable).
I would definitely say geld one, or sell one. One tip I have to keep in mind however - if you are going to keep stallions, can you keep them on pasture turn-out? And especially with their own mares. After breeding season I always turn my stallion in with his own mares for the following summer/fall/winter. This makes him MUCH MUCH happier and content as an old range gelding.
Even if not with mares, pasture turn out alone, or with an active gelding or two really helps the attitude of a stallion. My motto is, if they cannot be pastured out most of the time, either with their own mares, or geldings, they shouldn't be stallions. There are far too many great stallions out there that are extremely manageable that one shouldn't have to own one that is excessively aggressive.
Also of course, grain accelerates a horse's energy and active behavior - I don't generally grain my stallions unless it is winter time, or if I am working them. I do realize though the bigger operations generally grain their stallion(s) even when not working; I don't see any great point to this because they are much easier to be handled when not on a ton of high protein feeds.
Hope my 2 cents helps

Good luck and DON'T get hurt. NOT worth the risk.