I certainly would not rely on an extensive list of hand coded IP addresses in a hosts file since Google seems to have a propensity for changing IP addresses.
There are no real details of your network or how it's configured, but presumably you are using OpenDNS Home. In that case one option would be to enable OpenDNS for the entire network, block youtube.com (or all of the categories that youtube.com belongs to) and use a different set of DNS servers for the shared computer.
There are a number of potential weaknesses to this, including the possibility that users could manually configure DNS servers on their devices, or in the case of things like Android, turning on data saver effectively bypasses DNS options. Also, since Google uses such a complicated list of domains to reach their different services, often including different domains for different apps on different mobile operating systems, and sometimes different domains for different versions it can be difficult to track down the proper domains. Complicating that is the possibility for an app to use IP addresses instead of domains, in which case OpenDNS has no way of even knowing about the app.
