You could do the following:
Make the user as a LIMITED USER.
Limited User: By making a User as a Limited user, you can restrict the Child
from installing other programs on the computer.
Here is the procedure for making a Limited User Account.
1.) Go to Start
2.) Settings > Control Panel
(Alternatively you could click on Start > Run > Type "Control Panel"
without quotes.
Both these steps will take you to the Control Panel.
3.) Double click on Users and Accounts > Make a new user with your preferred
name. And in the Account type > Select Limited Account
(Or if you have already created the child account > make sure it is a
limited account).
With the help of the above steps the child cannot INSTALL .EXE programs.
Now We would like the child not to ACCESS the other EXE programs.
Note: I am not sure this part would work perfectly fine but you could give
it a try.
Implementing Group Policy:
http://support.microsoft.com/kb/323525
The above article should work with Windows XP as well.
Let me know if it worked out for you.
Regards