Blocking Youtube videos embedded into search

I have a family iCloud account and use Focus to limit the time my children spend on services like Youtube. I have a single rule which covers both app and website. However, the children has discovered that search engines like www.duckduckgo.com allow you to view YouTube videos, by-passing the Focus rules. The videos are embedded frames from youtu.be and youtube-nocookie.com, however adding these websites to the Focus rules doesn't do anything (I'm assuming Focus just applies to the original website, not the website of resources).

How can I limit or block watching YouTube on DuckDuckGo without blocking the whole search engine (which if set to the default search engine, effectively blocks Safari)?