The novice solution is to use "cloaking" where web site A loads a frameset document that loads web site B into a frame. That way the browser shows the URL for web site A the entire time since the frameset document doesn't change. Of course the browser is actually requesting the frame document from web site B.
If you were hosting both web sites on DreamHost, you could setup one domain to mirror a fully-hosted domain, or a domain to be a sub-set of fully-hosted domain.
Some people simply put forums on a subdomain, like main site is on example.com and forum is on forum.example.com - why won't that work for you?
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