It's not a problem that is hard to solve, except the constitution doesn't help one bit.
Just pick an English-speaking country, borrow its gun laws, use spell check to make the English an American version, vote for it and off you go.
No more dead children. Dead children is the right's cost of what they call freedom, but what they call freedom is, in fact, the elevation of property ownership and exchange rights over all others.
America inherited its idea of freedom and many of its citizens have never really understood it. The right's definition is lousy. That's the problem.
The real version of freedom with property rights is freedom within the law, freedom as far as you do no damage to others, freedom as long as it doesn't harm nature, freedom unless there are grounds for suspicion etc. Freedom is always qualified by its cost.
But the first Americans (ie English colonists) thought they could exist as if no one else did and resources were unlimited. Many on the right just haven't learnt the hard truth that this just ain't so once there are a lot of people. It's hard to discover something new. But freedoms must be shared among one another, which means including restrictions; and in acting freely you can damage the environment so you need to restrict that too.
I am afraid that a sensible definition of freedom wrecks the fun of acting with abandon.
My own suggestion for a cure is that all American children should be taught the happiness philosophies. They will discover that it doesn't come from property rights, at least once you have a sufficient amount of it to survive. Like Jefferson, start with Epicurus.