I have to run a WordPress site served via Apache2 & Java-based webapp using Tomcat on the same server.

When users come to example.com or example.com/public-pages they need to served from WordPress but when they come to example.com/private-pages they need to be served from the Tomcat.

I have asked this question on serverfault where they suggested using different port, different IP & sub-domain.

I want to go for different port solution since it will mean I need to buy only one SSL certificate.

I tried doing the reverse proxy method by having the following in my default-ssl.conf

    <VirtualHost _default_:443>
            ServerAdmin webmaster@localhost
            ServerName localhost:443

            DocumentRoot /var/www

            <Directory /var/www>
            #For Wordpress
                    Options FollowSymLinks
                    AllowOverride All
            </Directory>

            <Proxy *>
                    Order deny,allow
                    Allow from all
            </Proxy>

            ProxyRequests           Off
            ProxyPass               /private-pages       ajp://localhost:8009/
            ProxyPassReverse        /private-pages       ajp://localhost:8009/


            SSLEngine on
            SSLProxyEngine On


            SSLCertificateFile      /etc/apache2/ssl/apache.crt
            SSLCertificateKeyFile /etc/apache2/ssl/apache.key

    </VirtualHost> 

As you have noticed I am using mod_proxy_ajp in Apache2 for this. And that my Tomcat is listening to port 8009 and then serving content. So now when I go to example.com/private-pages I am seeing the content from my Tomcat. But 2 issues are happening.

1. All my static resources are getting 404-ed, so none of my images, CSS, js are getting loaded. I see that the browser is requesting for the resources using URL example.com/css/* This will clearly not work because it translates to example.com:80/css/* instead of example.com:8009/css/* & there are no such resources in the WordPress directory.
2. If I go to example.com/private-pages/abcd I am somehow kicked to the WordPress site (which obviously displays a 404 page).

I can understand why #1 is happening but have no clue why the #2 is happening. Regardless, if there is another clean solution for resolving this, I would appreciate y'alls help.