Any ideas?
very hard to make,
I assume everyone can work from every PC. That means you need to have login records from the PC (assuming the do not surf on each others account)
Tracking which PC visits which URL is slightly simpler but still beyond an Arduino.
Only the router in the house sees all the traffic so writing a filter for router software might be the most obvious solution. Another solution which comes in mind is writing a keyboard caption program and install it on every PC, not trivial but many virus makers do so at least it is possible.