Prevent users from changing LAN settings
First Try this:
By the way test this: first remove your child account from Administrator
1-Right Click On Computer -->>Manage -->>Local User And groups\User
2-By default your Administrator User is disable and there is another user which you create during windows installation for example it's Jack
3-Right click on Jack and select Properties
4-In the Member of Tab remove the "Network Configuration Operators" from the user and click Apply and OK
5-Restart your Computer
Hope it is work for you Prohibit Access to LAN Connection Properties
check this on ServerFault How to disable Tcp/Ip settings in windows 7 via GPO?
and this at microsoft technet Configure network connection restrictions with Group Policy