Hi Mark,
I've checked your profile and some logs and it appears that youtube is blocked, and your child should not be accessing it, but to help you more we will need some more information about your account. For privacy reasons, it may be best to give us a call on 1300 398 326 or send an email to support@familyzone.com with as much information as you can, and we can help troubleshoot this with you further.
Mark Pearson