Age 3 is a little early, as children of that age do not yet have an inclination towards discipline, focus, etc. - they are still learning the basics of socialization and behavior.
However, once they get to 4 or 5 years of age, you might consider Gracie Jiu-Jitsu if you have an academy nearby. They have a highly developed curriculum called Bullyproof, which is intended for children ages 5 - 13. But 4 year-olds seem to be regularly admitted.
Children up to 7 years of age, participate in a class called Little Champs:
The Little Champs program is for kids 5-7 years old (we offer private lessons for children ages 3-4). Using our time-tested “Gracie Games,” we teach the Little Champs basic self-defense techniques while instilling the foundational principles of leverage and control. The secret to the success of this program is that we make the lessons so fun that the kids beg for more! Once a child masters all ten Gracie Games, they advance to the Jr. Grapplers program.
Graduating from Little Champs, kids 8 years and up move into Junior Grapplers:
In the Jr. Grapplers program, we focus on 33 non-violent self-defense techniques that teach children to “neutralize and negotiate” with the bullies. Verbal assertiveness strategies are a major portion of this curriculum. A child needs absolutely no experience to start, and we guarantee a noticeable increase in your child’s confidence within a few weeks!
As your daughter comes of age, Gracie Jiu-Jitsu also offers Women Empowered:
Women Empowered is the official Gracie self-defense program for women. In this 10-lesson program, we will teach you how to neutralize the 15 most common attacks ranging from having your hair grabbed to being pinned to the ground by a weapon-bearing assailant.
Gracie Jiu-Jitsu is not concerned with competition, and has a bully / street defense focus.
On the competition side, our new home for Brazilian Jiu-Jitsu training is a Lucas Lepri Association academy. Their curriculum for children is not only applicable to bully / street defense, but also allows for a focus on sport oriented Jiu-Jitsu if desirable.
They have classes for children 3 -5 (Little Champions), 6 - 9 (Junior Champions), and 10 - 13 (Junior Champions II).
To select a martial art for our son, we researched numerous styles (Shotokan Karate, Taekwondo, Mudo, Kung Fu, and Gracie Jiu-Jitsu), and attended classes in each. We ultimately settled on Jiu-Jitsu because of its nature and reputation for being the gentle art. Unlike Krav Maga and the other classes we attended, Brazilian Jiu-Jitsu, for the most part, is a non-striking art. It relies on intelligence and leverage over brute force. It teaches techniques that instill options for de-escalating confrontations and avoiding harm to the adversary, which is prudent on the playground.
My son, who is now 8, has attended the Jiu-Jitsu schools mentioned above, and has benefited tremendously from both disciplines in Brazilian Jiu-Jitsu.