I'm still not 100% sure which way your issue is.
If you want it so that when the browser sees something like
<link rel="stylesheet" href="/styles/main.css" type="text/css" />
It requests the main.css file that tomcat hosts at /app/styles/main.css
Try:
ProxyPass /styles http://localhost:8080/app/styles
ProxyPassReverse /styles http://localhost:8080/app/styles
ProxyPass / http://localhost:8080/app
ProxyPassReverse / http://localhost:8080/app
Conversely, if you want it so that when the browser sees something like
<link rel="stylesheet" href="/apps/styles/main.css" type="text/css" />
It gets the main.css file that tomcat hosts at /styles/main.css
Try:
ProxyPass /apps/styles http://localhost:8080/styles
ProxyPassReverse /apps/styles http://localhost:8080/styles
ProxyPass / http://localhost:8080/app
ProxyPassReverse / http://localhost:8080/app
In either case, Apache will match in the order stuff appears in the config file.