I included several URLs in my router website filter to prevent my son from going there. I use OpenDNS which filters out a lot of the known garbage, but other websites are questionable.
Anyway, I have seen on Twitter and elsewhere that there is an abbreviated or tinyurl method of shortening a website to a few characters. There's a technical name for this which escapes me.
So suppose I want to filter out http://donteventhinkaboutgoingtothisdomain.biz.com and put that URL in my router's website filter, will I also have to somehow figure out the abbreviated forms of the URL and include them? I suspect that these abbreviated URLs are automatically generated by Twitter or whoever, and random.
That's a good question.
I just used tinyurl.com to shorten https://www.whatismyip.com/. It gave me http://tinyurl.com/2bxhz as a result.
When I click on the tinyurl link, it's converted to https://www.whatismyip.com/ so if you're blocking https://www.whatismyip.com/, then you don't have to worry about it in this case.
I'm not sure how other url shortening services work, but if they convert a short url to the full url, then you should be fine.
I've used a program in the past called CCProxy. It's free for up to 3 users. It let's you set an allow list, or a deny list. Plus it also keeps log files of all surfing activity. I ran this for businesses so I would review the logs and add sites to the block list as they came up. It might be more flexible than your router...but not sure.
You could look at Web filtering software. Or devices. They examine the actual network traffic to determine it's source. One we set up at work would block (for example) Facebook, regardless of the URL used. There are facebook proxies out there for bypassing social networking blocks, and since this one looked at the packets to recognize FB content, it blocked out even other URLs.
These appliances are not cheap. But you could try an old PC and something open source like vyatta.