Unless the 2 subdomains share a document root (or one is in a subdirectory of the other), then you can't do it without a proxy of any kind, with a [P]
in htaccess or setting up a reverse proxy using ProxyPass
(note that both use mod_proxy). There's no alternative solution that's strictly apache. You could write a script to load the pages of the other subdomain and park it on the first subdomain, but that's proxying as well, you're better off just using mod_proxy or one of it's extensions (like mod_proxy_html), which handles internal url rewrites of redirect locations, and cookies. An example of a non-apache solution would be mounting one subdomain's document root into the other and using mod_rewrite.