How would safe storage laws prevent this? They would just result in another charge for the mother. You really think someone who leaves a gun around with a 6 year old with behavioral issues would lock it up just because of a law?
The implication is that you actually enforce the laws after you implement them, rather than just implementing them as a way to add a charge. For example in my country police will come to inspect my house at least once a year to make sure im storing them properly and if a neighbour complains or something they will also make an unschedules checked.
I get American gun owners would take this basic safety precaution as the deepest violation of a tyranical government and would shoot a cop before they let them inspect their home for safety, but my point is if they did agree to sensible safe storage legislation this wouldnt have happened