Hello,
Thank you for visiting Microsoft Community and providing us with the detailed description about the issue.
As per the description, I understand that you are experiencing issue with you want to know “how can a child under parental controls install software without parent’s
authorization”.
I certainly understand your concern and will try my best to help you.
I would suggest you to refer to the article provided by
“Lonnie_L” posted on August 24, 2013 in the following Microsoft Community link.
Family Safety: Frequently Asked Questions
http://answers.microsoft.com/en-us/windows/wiki/windows\_other-security/family-safety-frequently-asked-questions/5672f7b2-e3c0-498a-9a6c-c9cab39f68e5
You may also refer to the article given below and check if that helps.
Set the right limits for your child.
http://windows.microsoft.com/en-ph/windows-8/set-pc-limits
Set up family features
http://windows.microsoft.com/en-us/windows/set-up-family-safety#set-up-family-safety=windows-8
I hope this information is helpful.
Please do let us know if you need any further assistance, we will be glad to assist you.
Thank you.