I'm getting to a point where I'm in this same scenario as well. Not in a straight walled state, have 3 children. 7, 4, and 2 in age. My middle son is definitely left handed, my oldest and daughter is right handed, baby Walter is TBD, but odds would say right handed. All of my kids are big for their age and I expect that trend to continue. I was put behind a .270 when I was 9. Bang/flopped two deer that year but went the next 2-3 being recoil shy.
I specifically remember shooting a doe with a .243 that we didn't find. Most likely a gut shot. Again, I was recoil shy too and wasn't given enough opportunity to practice with a small cartridge, let alone the one I was hunting with.
All of this is to say, I will be looking at a single shot rifle for my kids, but am thinking more along the lines of a 6.5 CM, 7mm-08, or even 308. I've got the suppressor already.
While I understand the logic behind a .223, larger diameter does equal larger hole, which in turn equals faster blood loss. There's no denying that. And kids are kids. Mistakes will happen, shots will get pulled, shot angles not always ideal, bones can deflect.
That's my 2 cents.