(Just call me Speedy Gonzalez, love that little mouse!)
Hmm, the domains being on different servers would pose a more complicated problem. But for future reference, here is what you could do if they were on the same server:
Same server, cross domain redirection
# vhost.conf for
http://sub.thisdomain.tld
# File: /home/httpd/vhosts/thisdomain.tld/conf/vhost.conf
#
# test for Gerhard to redirect/rewrite from
http://sub.thisdomain.tld to
http://sub.otherdomain.tld/dir/
#
# Need change
# from ~/vhosts/thisdomain.tld/subdomains/sub/httpdocs/index.html
# to ~/vhosts/otherdomain.tld/subdomains/sub/httpdocs/dir/index.html
#
# This will be a simple 'close' example, maybe not the *exact* you need, but should help get you
# on your way to the finished product. I know there are still some minor bugs with this code
# but it's just a simple example!
#
<IfModule mod_rewrite.c>
RewriteEngine on
ServerAlias sub.thisdomain.tld
# Rewrite sub.thisdomain.tld/index.html to sub.otherdomain.tld/dir/index.html
AliasMatch /index(.*) /home/httpd/vhosts/otherdomain.tld/subdomains/sub/httpdocs/dir/index.html
</IfModule>
####### End of this section #######
#
Separate servers, domain redirection
File: /home/httpd/vhosts/thisdomain.tld/subdomains/sub/conf/vhost.conf
<IfModule mod_rewrite.c>
RewriteEngine on
RewriteMap lowercase int:tolower
ServerAlias sub.thisdomain.tld
RewriteCond %{HTTP_HOST} ^sub.thisdomain.tld$
RewriteCond %{REQUEST_URI} !^/subdomains/sub/
RewriteCond %{REQUEST_URI} !error_docs
RewriteRule (.*) http://sub.otherdomain.tld/dir/$1 [L,P]
</IfModule>
Notice that we are using a P (proxy) instead of R (redirect).
I tested this browsing to sub.mytestdomain.com and it redirected to othersub.otherdomain.com/somedir my browser still showed 'sub.mytestdomain.com'.
However as soon as you click on a link at the new site, the otherdomain apache (of course) changes the browser URL to reflect the new 'otherdomain.tld'. I suppose you could then write more rewrite code on the 'otherdomain.tld' server to take care of it on that end. (but that's a whole different lesson, class is dismissed)
The user's browser still shows the original URL without change.