I've been looking for an authoritative source on this subject. It seems that all the "experts" insist on shooting with the side of the dominant eye, even if that is opposite the dominant hand. After trying this, I personally disagree.
For me it feels too unnatural, and it requires too many deliberate, as opposed to natural, actions. In a situation of stress, it is generally agreed that you will be half as good on your best day. Using the non-dominant hand would put you at a disadvantage to begin with. Add stress to the situation and you might have a potential disaster.
On the other hand, I train with my right hand, though I'm left eye dominant. I do one of two things: either shift my arms slightly to the left to have use my left eye (like they taught me at Front Sight), or as I come up to the target, quickly shut my left eye and aim with my right. Either way, I can hit what I'm aiming at with good grouping.
Doing what the "experts" say, shooting with my non-dominant hand to take advantage of my dominant eye, I do not group well at all, let alone under pressure.
