Welcome to the JavaRanch, Al!
Tomcat is not a file server. You don't "copy files to/from directories", you create and deploy
J2EE WARs to it. The ROOT folder as it comes from the Tomcat website contains a WAR that's bound to the webapp context path "/". That WAR is in "exploded" (unzipped form). Other WARs are conventionally resident in directories under TOMCAT_HOME/webapps where the directory name determines the context path that that particular WAR is served under.
You are not actually working with a subdomain here, you're dealing with
Virtual Hosts. In a fully-qualified Domain Name (FQDN) the top level (first element) of the domain name is the hostname.
In the stock Tomcat, there's only one virtual host, known by its alias name of "localhost" and its default appBase directory is "webapps". Or more precisely, %CATALINA_BASE%/webapps. So the only thing wrong with your Host stanza is that you are trying to embed one appBase directory under another appBase directory. You need them on separate directory paths.
The secret of how to be miserable is to constantly expect things are going to happen the way that they are "supposed" to happen.
You can have faith, which carries the understanding that you may be disappointed. Then there's being a willfully-blind idiot, which virtually guarantees it.