I agree with Robert: in a real-world defensive gun use (DGU) we generally fight with the pistol one handed. One-handed shooting comes into play even more when moving or running. Believe me, when bullets start flying, I will be attempting to do both at the same time. That said, it doesn’t have to be a straight up choice between one- or two-handed . . .
In the video above, Mr. Phillips shows seamless transition between one-handed and two-handed shooting while on the move. Body and hand positioning is all about keeping the pistol pointed on target with the least disruption from our own movement. Generally, a pistol held in one hand will bounce around less than one held in two hands. Sort of like the gyroscopic turret of a tank.
Generally, when shooting to target on a right handed shooters 1-5 o’clock while moving, one handed shooting is the best way to maintain balance and keep the gun indexed on the target.
When shooting at a target to a right handed shooter’s 11-7 o’clock, the support hand comes into play since the gun has to come in closer to the body. The body should be pointed in the direction of motion, not necessarily at the target. The 7-9 o’clock is the most difficult direction for a right handed shooter to target since it is essentially over the shoulder.
Pulling the gun in close and getting two hands on it allows for reasonable hits without hitting one’s own left arm. Left handed shooting is probably better for these directions.