About the only thing I can think of is to setup an administrator account for the mother, and make the kids use a standard user account. In addition, enable the built-in Adminsitrator account and create a password for it so that it cannot be used without knowing the password.
Afterwards, she could setup Parental Controls
on their standard accounts. The hard part is to either setup the web filter
to only allow specified sites, or only block specified sites.
If she wants to allow the kids to run anything that runs elevated by default, then she could use the tutorial below to create a shortcut that will allow them to without them having to know the password. Elevated Program Shortcut - Create for Standard User
Hope this may help some.