I will admit to using an Uncle Mike's nylon holster for pocket carry. However, when I do, in addition to The Four Rules of Gun Safety, I add a Fifth Rule: Nothing goes in the pocket with the pistol & holster. Nothing. Not ever. That way, there are no keys or other items to slip into the trigger guard.
When I belt carry, I use a dedicated gun belt (an Aker B21, which is stiffer than a normal belt), and either a Theis IWB or a Desantis Speed Scabbard OWB. Both of those holsters are of the sort that Frank described. Both are stiff and completely cover the trigger area. I am confident that nothing will get into the trigger guard and cause an ND.
We were all new CC'ers at one point or another. Many of us (myself included) have kids. I understand your concerns about carrying with one in the chamber, and the dangers of handling firearms around children. Kids are naturally curious creatures. The best remedies of which I am aware for those dangers are : (1) keep the pistol under your control; (2) when the pistol is not under your control, keep it secured (locked up, separated from ammo, etc.); and (3) education of the child, when that becomes age appropriate.
With all of that said, I always carry with a round chambered. I carry a pistol for my safety, and for the safety of my wife and child. As allaroundhunter noted, a distracted parent makes for an easier target. There is a good argument to be made that you may need to draw your pistol while using the other hand, for example, to fend off an attacker, or to push your child behind you. If you'll search youtube, you can find a video of someone simulating an attack: (1) with a round chambered; and then (2) without a round chambered. I'd suggest that you go watch that video, but I do not have time to go search for it right now.