Pay very close attention to what bdc says. Especially point 1. However, no matter what firearm or ammo you use, you are responsible for where any bullet goes. If you fire a shot that does not hit what you aimed at and it hits anything or anybody else, you are responsible.
Given your scenario, the only .223 ammo you should even think about is a varmint bullet. They're designed to literally explode on contact. Mind you, unless, like bdc says, you're trained and exprienced enough to shoot that well at your kid, forget it.
In any case, no stock AR-15 is accurate nor handy enough. Don't even think Mini-14. I must admit, though, that I wouldn't think twice about taking a close range, high risk, shot with my Plainfield M-1 Carbine. I know exactly where the 110 grain HP will go and I know my rifle will do it. I've had it a very long time.
"...pistol grip..." Only? The absolutely most useless firearm on Earth is a shotgun with just a pistol grip. You have no control whatsoever.