I've not used Tomcat before, so I can't shed any insight on whether Tomcat is doing any of the processing.
Where is this "index.html" page that you want to load? I ask because in your first message, you mention that you set the DocumentRoot to /webapps/, so I was assuming you had an index.html in there. But, with the above configuration, anything in /webapps/ is autoredirected to /webapps/PCW/ with these lines:
RewriteRule ^/(.*)$ /PCW/$1 [R]
If that's your intention - is there a /webapps/PCW/index.html in there?