When you "pistol-grip" a shotgun, you turn it more into a "special-purpose" weapon. That's fine, of course, as long as that special-purpose scenario is something that occurs regularly enough in your lifestyle to make it worth reducing the overall versatility of a shotgun. I was taught the finer points of the PG shotgun by the U.S. Marshals Service a number of years ago.
Firing a pistol-gripped gauge requires an isometric type of a grip on the gun. Your weak-side hand grips the gun's forearm and pushes the muzzle toward the target...your strong-side hand grips the pistol-grip and pulls backward...countering the forward-pushing effect of your weak-side hand. This "isometric tension" between your hands is what absorbs the robust recoil of that 12-gauge shotgun shell going off. If you can manage that, in short order you'll find that you can (from a semi-crouch) raise the PG gauge up to about the level of your collarbone, and shoot rapidly and accurately at short range, looking over the top of the barrel at the target.
Please note that if you let your strong-side hand continually take the pounding of the gun's recoil, you will have some hairline stress fracturing in your wrist bones before long. Please note, too, that a proper, two-handed isometric grip on a pistol grip shotgun tends to freeze up your upper body and arms. Thus, to address multiple targets, you'll have to remember to keep the isometric grip and pivot your feet quickly left or right to bring the pistol-gripped gun to bear on the target(s).
Think about that for a moment. With a "normal" handgun (and remember, a pistol-gripped shotgun is simply an abnormal handgun) you can keep your feet in place and rotate your upper body (like a turret on a tank) darn-near over a 140-degree arc, especially shooting Isoceles-style. In the stresses of a high-speed, spitting distance fight, it's often an advantage to keep things simple and use techniques where your footwork will take care of itself, and not be something extra to worry about.
However, with a pistol-gripped gauge you've got to be conscious of your footwork. It isn't a big deal, really. It's a matter of pivoting on one foot to turn your entire upper body. Pretty much just like when you were taught to pivot on one foot or the other when passing a basketball. Truth to tell, that ain't a bad skill for a defensive shooter to have in any circumstances. But it's the key for handling a PG shotgun.
Practice. I practiced...in fact, I practiced so much with my 12-inch barreled PG 870, using the issued full-power buckshot ammo, that I got a nice case of bursitis in my strong-side elbow. Some naproxen sodium and having enough sense to acquire low-recoil ammo for practice finally cured that. In retrospect, I should have instead used low brass skeet loads while practicing my two-handed isometric grip on the gun and learning to pivot to address multiple targets.
You reduce the versatility of your shotgun when you pistol-grip it. A great deal, too, because a properly-buttstocked shotgun gives you the ability to accurately shoot different loads at longer distances, including slug loads. There's a place for a pistol-gripped gauge, but not for "general" use. If you have the time to really master a PG gauge, you can do wicked work. Just keep in mind that, to date, you've internalized the skills needed to shoot shoulder-fired guns, and one-hand handguns (even though you often use two hands on those, too). The PG shotgun is neither fish-nor-fowl in that regard, not a shoulder gun, and not a handgun in the normal sense...so you almost have to learn a third shooting style to effectively use one.
Just something to think about.