RapidSSL's Basic Certificate when purchased under
www.mydomain.com
also covers
domain.com
Whilst not wildcard, it does give you cover for the TLD and www subdomain.
Yes, you can redirect from a subdomain to another without an SSL error - we use this on many, many sites, just one example is:
https://www.theclientarea.info which redirects to https://sms-sagat.theclientarea.info
Without error.
A simple .htaccess rewrite will take care of it for you:
RewriteEngine On
RewriteCond %{ENV:HTTPS} !On [NC]
RewriteRule (.*) https://%{HTTP_HOST}%{REQUEST_URI} [R=301,L]
RewriteCond %{HTTP_HOST} !^www\.example\.com$ [NC]
RewriteRule ^(.*)$ http://www.example.com/$1 [R=301,L]
Any type of movement between HTTPS subdomains will work without error or prompt, be it POST/GET/.htaccess redirect
The only time it becomes an issue, is if you are redirecting from HTTPS to HTTP - then it will prompt you.