This debate has been raging for quite some time now regarding way to live with or solve opposite-eye dominance problems with shooters. As I, too, fall into this category, there are several options that have worked for me.
For handguns, I simply draw the pistol across my body with my right hand and align the sights with my left eye. In doing so, the right arm is pulled as far as the torso will allow, thereby acting as a rifle stock to stabilize the shooting platform. Unfortunately, this angle does tire the shoulder quite quickly, so when not shooting one simply lowers the pistol. Upon raising the pistol once more in this position, the sights generally return to the previous aligned position with a minimum of adjustment or movement.
With long guns, however, the situation is somewhat more complex. If the opposite-eye dominance is not overpowering, the shooter may be able to train themselves to shoot with the off-hand or weaker eye. If the dominance is more pronounced, there are several assistant devices such as stick-on blockers that can be placed over the strong eye, thereby forcing the weak eye to take on the effort of focusing. One may also wear an eye patch to accomplish this method. Otherwise, one may consider shooting from the opposite shoulder, though it should be noted that most people do find it difficult to shoot from the opposite side once they have trained themselves for a lifetime to be dominant with a certain hand.
As always, there are many ways to deal with this situation or solve this problem. No one solution will work for everyone. Feel free to post your suggestions and consider any alternative that might work for you.
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I've been doing this now for years!
