There is a very vocal and select group of people who feel the mention of guns, weapons or even matters of personal-defense around a child is equivalent to child abuse. I personally raise my three daughters to respect and honor the use of firearms and ingrain the obligation of personal defense as a mindset. All of my children (minus my son, who is 2 years old) have a good understanding of safe gun handling and could easily use a firearm in a life threatening situation, not to mention go hands on, if assaulted by a person relative to their size.
I refuse to let my children grow up in a society that encourages victimhood; therefore to combat that, all my children train in multiple aspects of personal defense. It is my suggestion, if you do not already, teach and/or find an instructor who can teach your children real life personal-defense. (This also applies to firearms, if you are not much of an instructor or want someone more qualified.)
Unfortunately, most places that teach children are nothing more than an expensive day-care, where they punch and kick things. If they are not provided a way to test their developing skills with true resistance, they may be developing a false sense of confidence while earning that new colored belt.
It is hard not to get lost when looking for training with all the places around today. But there is one key component to real quality skill development and that is sparring. Look for a place that provides a good safe sparring outlet. If done the right way, sparring is a way for your child to test, refine and develop serious skills that can be trusted under stress.
I pray that my children never have to defend themselves, but if the circumstance should ever arise, I know that they will have some good training to fall back on. At least they will have the choice, unlike those poor children without a personal defense mindset who are doomed for victimhood.