Can anyone suggest .htaccess code that will redirect https://domain.com to https://secure.domain.com ?

If I was redirecting to https://secure.example.com I would use

RewriteEngine On
RewriteCond %{HTTP_HOST} !^secure\.
RewriteRule ^(.*)$ https://secure.%{HTTP_HOST}/$1 [R=301,L]

Change secure on line 2 and 3 to your ssl subdomain. This is the code used to redirect non example.com to www.example.com, modified to work on a subdomain.
If put in the site root, it will redirect EVERYTHING. If you want it to redirect just one directory, put it in the appropirate folder

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