First off....why 2 forums? Why not 2 boards in one forum?
Simplest way to do this is to create a second virtual directory for the new forum (2nd). You'll need server access to do this, but should work just fine!
So..call one
www.mydomain.com/forum1 and the other
www.mydomain.com/forum2. As long as both are virtuals, both with own process control, you should have no problem.
HTH
.....the man in black fled across the desert..........and the gunslinger followed.....