Yeah, safety concerns and plain language are going to have to trump your desire to shield your kids from "forbidden" knowledge.
If you act weird about having a gun, the cop's first instinct is going to be to suspect that the reason you're acting weird about having a gun is that there's some legal reason why you shouldn't have a gun. The possibility that you're acting weird just because you don't want your kids to know that you're in possession of something that's legal for you to possess isn't going to be on the officer's radar. At all.
There is a good chance that the officer has kids of his own. He obviously has gun(s) and his kids know he has gun(s). The idea that kids need to be protected from even the knowledge of guns is going to be completely alien to the officer. Even if the officer isn't a "gun" guy with a personal arsenal, his sidearm, at a minimum, is just part of his world. Of course his kids know he has it, what it's for, and not to touch it.
Some, maybe even most, cops will be cool about your carrying a gun with a CCDW and not make an issue. Hand over your CCDW with your driver's license and say something like "I just want to let you know, sir or ma'am, that I am carrying." If the cop is cool, he might say something like "Where is it? Keep away from it. Thanks for letting me know, etc." and that would be the end of it. Your kids would never know.
But, if the cop isn't cool about it, or feels the need to investigate it further, or asks you directly about it, then being weird or coy about stuff will just excerbate a stressful situation. Use plain language and avoid any potentially tragic miscommunications.