Sorry, I can't comment so I've posted this as a 'answer'.
A few things to consider:
Is a 13 year old or his friends going to notice a process in taskmanager that shouldn't be there? (for example a second explorer.exe, svchost.exe etc.)
What are you trying to actually achieve as there may be other ways to do what it is you want. Are you trying to block them from going on certain sites? Are you trying to monitor what they do? Are you trying to prove to your mum what they are doing? Something else?
Unless you are trying to block them, will they care about anything you may have running? Would they bother to look for 'logging' software running on the PC? I would guess that they wouldn't bother to even open task manager unless the sites weren't working.
If you are trying to give proof or monitor your pc, running a VNC service in the background allows you to connect a viewer from another computer so that you/your mum can watch a live view of what they are up to.
If you want to monitor the sites then you have a wide range of options: keylogging software, browser logging software, proxy software or logging software on your router
If you want to block the sites then you also have a wide range of solutions: hosts file, dns based blocking (e.g. openDNS), blocking software on the pc (e.g. netnanny), blocking software on the router, etc.
Remember: If you are trying to block sites remember that nothing will block 100% of websites. You will only achieve 1 of 2 things: (Ideally) it becomes too much effort trying to find sites not blocked and they use another computer for their porn -or- they persist and find a way around it/to disable it/sites that it doesn't catch