This reply is opinion, based on experience to date...
My twin daughters and I started scuba diving together last summer, at age 12 then. They are excellent swimmers, having been on the swim team since age 6, and are comfortable in the water. During the OW course, they had to demonstrate all of the required skills and complete all of the knowledge reviews, and then they had to complete all of the open water dives in 7mm neoprene, hoods, gloves, wearing almost their body weight in gear! They weren't given their C-cards, they earned them.
Having said this, one of the girls and I have done about 24 dives together since June 2002; the other sister has done only 9 dives. They both know their abilities and limitations, and among those, they know that the OW limitation is 60 feet, AOW 70 feet. Have we exceeded those limits? No, not yet, because our instructors strongly imparted to them (and me) to not exceed the limits of our training until we have additional training and experience. Plus we practice our skills with just about every dive trip we do together, especially at the local quarries (skills such as AAS, signals, remove/replace scuba unit).
They have earned the respect of their instructors and DMs over the months, as well as my respect. Just because they're "kids" doesn't mean they won't respond properly in an emergency anymore than an adult would respond properly.
I wouldn't consider taking them deep until they've had deep training. Multiple dives I certainly do do with them.
Hope this helps.