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