Why do you use the built-in windows child restrictions?
There are tons of softwares much better than the Windows tools, where you can allow the use of some softwares, some operations, while blocking other ones.
Google: internet addiction software, or anything like that, and you have many suggestions to try.
There are 2 kinds of actions you can do: preventing use of the computer outside of specified periods of time, and preventing the use of the internet or the use of some software.
The kid shouldn't use the admin account, it should be a normal account, but no need to have the password for anything if you use the normal account + a dedicated software normally.
As I recommended 2 ways to do that.
Method 1
Preventing use the computer:
You can use any of these class of softwares or devices:
Parental control softwares, sofware firewall or hardware firewall.
Hardware firewall seems more complex, and require you buy a device, so I just mention it, to let you know how it works:
How to prevent unauthorized computer access
HackerMost users are interested in taking steps to prevent others from
accessing their computer.
**Hardware firewall** - A hardware firewall is a physical device that is connected to your network. Often, many users who have a home
network can use their network router as a firewall solution. (...)
Software firewall - A software firewall is a software program that you install on your computer to helps protect it from
unauthorized incoming and outgoing data. Keep in mind that a software
firewall is only going to protect the computer on which it has been
installed. Additionally, many antivirus scanners include their own
version of a firewall program
Source: http://www.computerhope.com/issues/ch000464.htm#firewall
These kind of methods can be used to prevent access to specific softwares (e.g games), or to prevent specific software to access internet (e.g online games, browser, etc...), preventing any downloads or internet browsing.
Method 2:
Preventing the use outside specified period of time:
You can use specific specific softwares (parental control) or use firewall softwares with blocking based on time restrictions.
As an example, you have K9 protection.
http://www1.k9webprotection.com/support/kb/k9126.html
You want to know how to configure and test the Time Restrictions
feature in K9 Web Protection.
(...)
K9 Web Protection can restrict web access according to a daily time
schedule you customize. Note that currently this will only affect web
site browsing, not Chat/IM, P2P or other internet traffic.