There are various forms of Martial Arts and so check out what is available and what is more fitting for your family.
The organisations below are the ones I could find that catered for children.
Blue Mountains Martial Arts Centre: Based in Leura and runs Mixed Martial Arts (MMA) classes for children including karate, Arnis, Brazilian Jiu Jitsu, boxing and weapons. www.bmmac.com.au
SJJA Blue Mountains: Based in Springwood they teach Jiu Jitsu with session for both children and also family sessions. www.sjjabluemountains.com.au
Blue Mountains Taekwondo: Based in Blaxland they run classes for ‘Little Tigers’ and also Junior classes. www.bluemountainstaekwondo.com
Karate NSW: There are classes running in both Katoomba and Blackheath on various days. www.karatensw.com.au
Total Self Defence Academy Blue Mountains: There are classes running in Blaxland, Springwood and Winmalee. www.totalselfdefence.com.au
Western Warriors Martial Arts: Based in Blackheath classes combine Jitsu and Judo with classes for the whole family. www.westernwarriorsmartialarts.com.au