I don't have kids...
However, when i was 11 my dad took me for a couple short rides. It was my uncles 1997 Fatboy (the same one I bought from him years later, and still own and ride) and we only went around the block a couple times. I kept bugging him that I wanted to go for a ride, so he took me. Completely stock setup, going slow as hell. I could tell he was afraid I would fall off.
I've ridden with little cousins on my bike, again just for short rides. My rule of thumb for children riding with me is....if they are big enough to reach the passenger pegs and wrap their arms around me they can go.
"Leader of men, teller of tall tales, legend in his own mind, U.S. Marine extraordinaire, stream fordable, air dropable, beer fueled, water cooled, author, history maker, lecturer, traveler, freedom fighter, defender of the faith. Wars fought, tigers tamed, revolutions started, bars emptied, alligators castrated. Let me win your hearts and minds or I'll burn your damn hut down"