Most gun owners do not think of handgun shooting as a martial art. I am not sure what they actually think of it, but it certainly involves ego and a distinct disdain for anyone who would tell them what to do even in the face of a terrible shooting display.
You do not need some sort of paid service for this.
Take a friend with you when you go shooting. One shoots and the other plays the part of instructor. You can continuously trade off and evaluate each other throughout the session. Try learning Paul Sharp's material using this method.
You could also watch cop shootouts and see that there's really no right forms or moves.
There are indeed correct forms and moves that one can do. If there were not, then every cop would hit every time and the criminal would stop their attack immediately. The "form" is dependent upon context. The form used by an NRA pistol competitor is vastly different from self-defense shooting while moving. The following focuses entirely upon self-defense with a handgun, applies to all handguns, and can be used with or without movement and with or without a sight picture. This is not point shooting and the demonstrations are sighted shooting.
You can use this same technique while point shooting, which is required for shooting while moving fast under tight time limits. The time limit is determined by bullets coming toward the shooter which happens to be the reaction time of the target (OODA loop and all that). Even within point shooting, there are many forms (Half Hip, 3/4 Hip, straight arm, Metal-n-Meat, to name a few). We're not concerned with those here. This is a set of physical instructions that may be employed from any angle, at any speed, with or without sights.
Paul Sharp's "Recoil Mitigation"
(Rangemaster Tactical Conference 2016, Memphis, TN)
Training points:
Mitigating muzzle rise from the wrist (Videos 1-4):
1) Lock wrist on each hand that is touching the gun
2) Hard pinky finger pressure
3) Push thumb(s) forward hard
4) Proper grip: High in the tang, high under the trigger guard. Forward thumb on support hand. Check by placing trigger finger and support hand thumb on frame. They should be equal on the frame (point up to check).
Test by attempting to bend the wrist upward. Instructor places finger on wrist tendon to verify (Video 5). The shooter will tighten up and prevent as much movement as possible.
Mitigating side to side muzzle movement (Videos 6-7):
1) Tighten the elbow of each hand on the gun
2) Tighten the shoulder of each hand on the gun
Test by attempting to move the gun in a circle.
Mitigating gun push backwards (Videos 8-13) :
1) Use hard push-pull. Some people think push-pull doesn’t work in a fight so an alternative is to bring your elbows down a bit to pinch your palms together. I have been experimenting with torquing my elbows. It's not up or down; it is turning the bones of the forearm inward. This tightens grip well and locks things in. It works with one or two handed shooting, though two handed shooting is universally more stable. But, in a fight, you may be using one hand to fend off an attacker.
2) Push from the primary hand shoulder.
3) If support hand is on the gun, pull back into the primary hand.
4) Nose over toes. Stance is aggressive and nose should be over or slightly past the forward toe. There are no stances in a fight, but this is the optimal case.
Instructor tests by pressing with continuous pressure against the shooter's hand. Their head should not move very much. The instructor should watch for head movement by comparing to a static item in the background. Properly done, the shooter's head will barely move during recoil. Watch the shooter's toes. They should not rise.
Video 14 is a summary of training points.
The only addendum I have is that you can pinch your palms together a bit to tighten your groups up at speed.
That is a rather large flaw.
