If your users are having DNS problems, they are unlikely to be able to resolve any host names at all. In that cause, no mirror will help, as any mirror still requires a DNS lookup to resolve (http://something/some-page) into an IP address.
So the fail safe way is to give the address raw (eg 126.96.36.199/page). However, this doesn't work with virtual hosts. In this case, the IP address that superuser.com resolves to is also used for stackoverflow, and the web server doesn't know which website the request is for.
So, starting with
We can bypass a DNS lookup by using
188.8.131.52/questions/231977/how-do-i-diagnose-not-being-able-to-reach-a-specific-website-as-an-end-user ... but on a webserver with multiple sites, it will resolve to the default website (and in this case, will result in a page on stackoverflow).
Last step then: On the webserver, you would then have to set up proxy rules to redirect the request. By changing the url to something like 184.108.40.206/superuser/question, you can setup a rule on the webserver to foward any requests to the correct website.
Your resulting url then looks like
This will require a change in the setup of the server to redirect the url to the correct virtual host. It will also completly bypass any DNS problems.