The parents should be prosecuted. They should lose their gun ownership rights, permanently.
I am a solid 2nd supporter and a life member of the NRA. I don't believe in waiting periods, assault weapons bans, ammunition serial numbers, "smart guns", or any of it. But I do believe in responsibility. All gun owners are responsible for the safe storage of their weapons. Period.
There are inexpensive gun locks and quick-access boxes which would allow you to get your piece out quickly if you need to. I myself have a fantastic pistol safe with a Simplex pushbutton combination lock. I can get my .45 out and ready to shoot in about 10 seconds.
There is no excuse, ever, for leaving a loaded gun around where a little kid could find it and hurt themselves.