Really short version, edit your wp-config.php;

define('FORCE_SSL_ADMIN', true);
define('WP_HOME',        'http://www.blog-url.com');
define('WP_SITEURL',     'https://secure.host-url.com/~account/wordpress');
define('WP_CONTENT_URL', 'http://www.blog-url.com/wp-content');

This should allow your site to have it’s own address, yet enable secure login via a shared ssl.

The longer version, I really don’t care to explain, but if you break something whilst changing the “WordPress Address (URL)” (WP_SITEURL) and “Site Address (URL)” (WP_HOME) in Settings->General, you’re in a world of pain. Easiest form of recovery is by overriding the values in wp-config.php.

Again, I just want to make a point of “Site Address” uses the WP_HOME variable, “WordPress Address” uses the WP_SITEURL variable. I believe this naming is counter-intuitive, because I actually spent time figuring it out.