RewriteEngine on
RewriteCond %{HTTP_HOST} ^(www.)?myotherdomain.com.au$
RewriteCond %{REQUEST_URI} !^/aliases/myotherdomain/
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule ^(.*)$ /aliases/myotherdomain/$1
RewriteCond %{HTTP_HOST} ^(www.)?myotherdomain.com.au$
RewriteRule ^(/)?$ aliases/myotherdomain/ [L]

Rewrites url to appear like the additional domain appears independently hosted, however, only appropriate for a temporary web page as other pages throw an error.

Host additional domain in subdirectory

htaccess

Apache