A basic mistake a lot of parents who own firearms have made in the past though is (Perhaps inadvertently) creating the ultimate "Forbidden fruit."
Winner winner, chicken dinner!
We are members at an outdoor range that has skeet shooting, rifle ranges, pistol ranges, archery ranges and fishing. My kids know that we can go shooting anytime they like to fish, shoot or practice archery. They have had hunter safety classes, firearms safety training and, pretty much any day of the week go shooting if they like. Every time they go they are reminded of safety rules, have to practice them and have to clean the guns when they are done.
Guns are absolutely no mystery to them and there is no fascination with them whatsoever. They are both excellent shots, know safety inside and out and have never attempted to play with a gun unsupervised. There is no mystery there.
Sounds exactly like my upbringing, and you are right. The key word is in all of this is responsibility. I learned a very long time ago that handling a weapon of any sort was a privlege that carried a weighty responsibility.
In looking over your photographs I was concerned that there was no protection from other shooters and their children.
Since this appears to be a public range I assume (big assumption which I would not make if I was actually there, I'd confirm it before using the range) that there is a range warden on site to insure safety.