How do I redirect subdomains to a different port on the same server?

Solution

Here is what I finally came up with after being set in the right direction by Miles Erickson. I wanted the address bar to reflect the original subdomain/domain of the request and not the redirected server and port, but he put me on the right path to Google up a solution using VirtualHost and I finally found a solution that included the use of mod_proxy.

First, make sure mod_proxy is enabled:

sudo a2enmod proxy
sudo a2enmod proxy_http
sudo a2enmod proxy_balancer
sudo a2enmod lbmethod_byrequests
sudo systemctl restart apache2

Next, add the following to your site config (e.g., /etc/apache2/sites-available/000-default.conf):

<VirtualHost *:80>
    ServerAdmin [email protected]
    ServerName dev.mydomain.com
    ProxyPreserveHost On

    # setup the proxy
    <Proxy *>
        Order allow,deny
        Allow from all
    </Proxy>
    ProxyPass / http://localhost:8888/
    ProxyPassReverse / http://localhost:8888/
</VirtualHost>