Help, i desperately need help

[theeos]

I have 2 teenage daughters, and I suspect they are involved in inappropriate activities in the internet. They both have computers in their rooms. :
One of them has internet connection through a network cable plugged into the DSL router. She her computer uses the windows operating system. She also uses microtrend internet security. I strongly suspect that she's having inappropriate late night conversations with yahoo messenger. I know she deletes her chat log every night and clears her browser history.
Daughter #2 has a network cable running from the first computer's router to her wireless router in her bedroom. She uses her laptop with a  wireless network adapter. Her computer is running Windows XP, and she also uses microtrend internet security. She is also misusing yahoo messenger, she deletes her yahoo message archive every night and clears her firefox browser history.
They both deny any inappropriate activities. I don't want to take away computers or completely shutdown internet access unless I have solid proof that they are actually doing something wrong. My laptop is loaded with the latest Debian distro, and I have very limited programming skills. Since I'm an administrator on both routers and both computers, it seems that there is something I should be able to do to monitor their internet activities, just long enough to be sure that nothing inappropriate or dangerous is going on. My daughters are 15 and 16, and are reasonably computer literate. I tried pearanal controls, but they know how to turn them off. Please help, There must be a way for me to monitor computer traffic in my own house.
Thanks in advance for any help you might be able to offer.
Don

[Shark Fin 101]

If you want advice... here you are...

They both have computers in their rooms.

This is the first thing that caught my mind. Surely it's not necessary to have them in their rooms. Family room, kitchen table, etc. are better locations.

Solution #1:
Depending on the router you have, you can turn on the logs... meaning it'll log anything that goes through it. It might show it in cryptic format (e.g. IP addresses you'll have to look up), but it'll be an unclearable record unless they know the password.

Solution #2:
If they are clearing their history, then that's probable cause right there. Mention to them to stop clearing their history. You're the boss.

Solution #3:
Sometimes there are parental controls on the routers.... you might check those as well. This is the best option in my opinion.

Solution #4:There are dozens of webfilters out there... Besafe online to name one. Choose one, make up a password, and your problem is solved. Unless they know the password you can be fairly sure the problem is solved.

IM I'm not so experienced with... I'm fairly sure that #2 and#4 would solve it, but not completely sure.

I think the last two are the best solutions-- they communicate your love for them rather than distrust.