Its an easy thing. Taken from a third party we have some guyw aving a rifle around and letting children play with it. You're going to get a hard look at, at least in my area. Especially when its the scared to death mom calling.
Go out on a few calls sometimes. Many departments have a "citizen's watch" program where they will let you do a ride along with your local PD or sheriff. It'll probably take about an hour into the shift before you figure out that there is no "easy thing". You'll learn pretty quickly what every cop knows - there are two sides to every story, and that the truth is somewhere in between.
Your call of a scared to death mom claiming that someone is waving a gun will definitely get some attention. Once the neighbor explains what happened and the kids tell their side of the story, i.e., he was cleaning the gun and they wanted to touch it, he wasn't waving the gun around, the mom never saw the gun, etc, then the most that will likely happen is that you will be told to keep your kids out of the neighbor's yard. Of course, you can make up any lies that make you feel better and the neighbor can too. In that case the outcome will depend on who is the better liar.
If you don't want your kids touching guns then you should try taking a little responsibility for their upbringing. 10 years old is plenty old enough for you to teach them not to touch a gun and to leave the area unless you are there, not to get in a car with a nice man with some candy, etc.