I think you've reached an effective compromise. Some rules are immutable, some are able to be interpreted, but you as the father must choose what is most appropriate for you and your son.

As a range officer and a Hunter Education/Safety Instructor, there were well defined rules that never changed, that were agreed upon by all the range officers and instructors, and uniformly enforced.

As an instructor, we had a three strikes rule. If the student was caught putting his finger on the trigger when he wasn't on the firing line and about to shoot, or if he could not say what the status of the firearm in his possession was in (safety off/on, round chambered or in the magazine) or if the student handed off or received a firearm without leaving the action open/checking the open action and acknowledging the exchange verbally. If a student pointed the muzzle at any time at another person, they were failed on the spot and the firearm was immediately removed from their possession. If they discharged their loaded firearm before the order to fire was given or after cease fire was ordered, they were failed the same as pointing the muzzle at someone.

At the range, the following resulted in a verbal warning on the first offense and dismissal from the range after the second time:

Handling firearms at the firing line while the range is cold (firearms that are cased and unloaded were excluded, so long as they were left in the case until the range went hot again).

Pointing the muzzle of a firearm anywhere but downrange while the range is hot (canting the barrel of muzzleloaders or to check/clear a muzzle was not a violation, so long as the angle did not break the plane of the firing line).

Reckless/careless behavior at the firing line.

Crossing the firing line while the range is hot.

Discharging a firearm for any reason while the range is cold was an automatic dismissal for the day.

Threatening other people at the range or disobeying the directions of the range officer would result in automatic dismissal for the day, and could have you talking to the sheriff if non-compliance/belligerence persisted. Your name was likely to end up on the black list as well.

Hunter's education groups subscribe to the nearly universal ten commandments of firearm's safety. My recommendation is that in addition to other discipline, every time your child commits an infraction, ask him to recite all ten commandments to you.

As for your wife, I can only say that firearms are a tool that you often only get one chance with. Their use must be held to a greater standard of care than pretty much any other thing your 8 year old will control. Shooting is to be considered a privilege unlike anything else in his life. He holds the power to take life in his hand, and must learn that shooting requires a mature attitude; something beyond simply having his playstation taken away when he behaves badly. His actions at that age must be well conditioned, and I would say your actions at his unintended discharge are germaine and appropriate. After shooting, I would say calm and constructive discussion should follow, and that would be your responsibility to establish that, even if he loses his cool.

Hopefully some of this has helped you.