RewriteRule of .htaccess not aliasing the url

The most straightforward way to manage multiple domains is by using multiple virtual hosts in your Apache configuration. If you only have access to the Apache configuration via .htaccess, you will need to setup multiple re-write rules. This can be configured with or without restful URLs.

There is a fairly extensive discussion on multiple domains here:

Do be aware, however, that this will require mastery of Apache’s mod_rewrite directives and it is one of the more complex server administration topics discussed here.