ano said:
So, some warning, it will take you a few weeks to months to get this fully set up but it is worth the time. Some "consumer" level routers claim to have some of these features, but you'll be disappointed. Go for business-grade.
This. It's pretty simple to log/block website name lookups.
It's quite a lot more involved to get into logging/blocking the specific web traffic itself. More often than not logging/block of the DNS requests is enough. pi-hole has a great UI for this and runs easily on even a pi3.
Before I'd wander into the very complicated territory of active logging/proxying, I'd look at the simpler method of just checking the history on the browsers themselves.
If this is a parenting issue then you've got the two-pronged approach of you know you've seen DNS lookups for things... but magically the browser history doesn't show it? As the meme says " that's a paddlin' "
That's the approach I take with ours. Monitor what is coming across on the DNS and then "have discussions" about inappropriate use of the internet. To me, trying to take a 'block everything' approach just encourages misbehavior. I'd rather know and help guide, than be punitive and end up teaching them to hide things. But that's me, not everyone chooses to manage their kids the same way.