If it was a mistake, it was inexcusable.
Not really. Accidents happen in war. The Syrian border is a hotbed of gun smuggling and terrorist infiltration. Some Marines were killed there a few weeks ago, so there are bad guys in the region. It would make sense to an AC-130 pilot that if there are weapons being fired, it stands a very good likelyhood that they are under attack or an American force of some kind is under attack. Now, if the same AC-130 gunship was flying over a Seattle Mariners game and saw the fireworks display as an attack, and opened fire on Safeco field, killing fans in the ballpark, that would constitute what you call an "inexcusable" mistake. Oh, and shit happens.
If it was a gathering of hostiles, then it was still a mistake. Go kill the hostiles, not the children.
Uhmmm...I'm not sure how to answer this one. If there are a bunch of bad guys who are also really bad fathers and bring their kids around dangerous situations, then isn't the bad fathers to blame?