I'm a handgun and self defense instructor. I especially teach a lot of women, often novices, to shoot.
Most of them are not very strong in either hand. They must have a grip and stance that will provide the best and most stable platform for accurate shooting. Since self defense is not about target shooting, they mostly learn "point and shoot" at close range.
Most handgun instruction - usually by and for men - teaches an inherently unstable grip and stance which puts the gun at the full length of the arms.
Many of the men initially INSIST on holding the gun out at full arm's length. That's the way they were first taught, and they are shocked to find how much better control they have if they don't do that!
It is especially important when shooting one handed, no matter if it is the strong or weak side.
Take a look at
http://www.TacticalShootingAcademy.com if you are willing to rethink pretty much everything you ever learned about grip and stance.
Also look at the book, "Fist-Fire" Defensive Speed Shooting, techniques for self defense, executive protection and concealed carry
Might see some things that interest you!