One half may dominate the other in order to reduce the traumatized hemisphere's exposure. In essence, the person has two minds.
My Dad had a violent temper that he managed to control most of the time. His dad abandoned his family when he was born. His mom died when he was nine. He was almost abused in an orphanage and his older brother pulled a great escape caper to get them out of there. He then lived with the step dad who his mom remarried before she died of TB. The step dad had a violent temper.
It was very rare that my dad hit me but often threatened with the right hand while yelling. His right hand would be raised threatening my left side of my head. As a kid having done something I could not run away from the threat. There was no where to run to. I stood there and cowered especially on the left side. I have the distinct memory of seeing the left side of his jaw contract and bulge when he was angry. I wonder if it may be tied to why I don't tend to see the left side of other peoples faces. He wound up having to eat in the other room during dinner so we there would be some peace during the meal.
I was in trouble as a kid often. I think I was the favorite of three brothers but I was also in the most trouble for doing stupid stuff. There was something in my attitude that pissed him off. He said later in his life he often got the feeling that I thought he was wrong. My feeling was I was always trying to understand the 'why'. I never entertained the thought that he might not be right until later in life. He was also very affectionate when not angry and sincerely loved us. I remember as a kid being worried that he would not come home but scared when he did.
If there is a duality of the mind my right and left sides may perceive threats differently. However I do not think this is an abnormal response but a more accurate description of who I am.