You can run ezpublish as php cgi or apache module, but last is recommended
if you are running another ezp setup on the same web server without using php cgi URI, I guess that you can force the ofending ezp site to run the other way
A couple of questions:
Are you using Virtual Host to host your several ezp setup ?
Have you compiled your offending ezp setup using ezp command line compiler , case yes, what options are you using ?