Regardless of the triggers NOBODY in their right mind chooses to murder their wife and small child.
Yes they do. History proves otherwise. Plenty of people who aren't mentally ill kill others. I don't know why people are so convinced that you have to be mentally ill in order to do so, not to mention that you can be mentally ill and still know what you're doing. It isn't as black and white as mental illness = lacks capacity.
My friend was stabbed to death, with numerous stab wounds, by her abusive partner and left for her young daughter to find when she returned from school. He had no history of mental illness. He did have a history of being an abusive angry twat though.
A family friend's daughter was raped and strangled by another abusive, egotistic and angry man who would be known as an incel if it happened now. No history of mental illness. Just a history of being an angry misogynistic piece of shit.