We know terrorists are targeting and killing small children. Children die by being "in the way" for the killing of adults by terrorists. From the news, it seems that lots of innocent people are in the way of the combatants or are deliberately targeted by violent groups. These include grown men and women as well as children, if they accompany parents. Like in Iraq or Afghanistan many children were targeted by terrorism, violence and war. Like when the violent groups kill children and innocent adults.
In the U.S., the policy seems to be to protect the most vulnerable public places, and these are government buildings, utilities, schools, etc.
I don't see any concentration of protection for U.S. children. With regard to them, American also need more protection against U.S. pedophiles and U.S. crazy gunmen.
Since human behavior is a combination of genes and environment ("nature and nurture"), our proposed solutions might help the environmentally induced aggression, but not our genetically induced aggression. Therefore, aggression will always be with us, not matter what environment is established. However, considering the latter as a way to at least reduce aggression somewhat, consider that asocial behavior of all kinds is a consequence of the combination ignorance, aggression, formal education partially helps employment partially helps good parenting helps but nobody pays any attention to that source of our problems, so what you propose are only partial solutions.
As for "good government", that would help all three problems indirectly by promoting employment, education, parenting, etc., but that concept must be translated into specific programs to be meaningful.
Violence as "the murder of innocents", i.e., non-military, non-police, and non-politicians. Army is used by the government to protect the general population from foreign and domestic aggressors.
Armies and police can defend the country against violence and terrorism, but are ineffective against isolated attacks. Outside the country, an army can assist to defeat terrorism, but cannot accomplish that alone because terrorists are not found in armies. Only way to defeat terrorism and violence is to assist police and intelligence. However, it will take a long time.
These groups can survive longer if they become immune within a country. That is why it is important to bring them to justice. The deaths and the property losses after attack cannot be restored completely no matter how much money other countries send.
We certainly can defeat violence and terrorism if we spend lots more time, and create awareness on peace, love, freedom to do so over a long period of time. Whether or not we will be willing to make these sacrifices to achieve these objectives is indeterminable at this time.