If I understand your question correctly... I'm going to take a sloppily worded stab at part of your question....
I don't know why they want to take the HTTPS off of the subdomain, but adding it onto the main site is probably because customers are asking why we don't have HTTPS there when our competitors do. The main site has a lot of links to the login, but the login page itself has HTTPS.
While you definitely would want to have log-ins, etc, on https, making the entire site https, IMO, is not a good approach.
The reason for keeping one subdomain as a secure subdomain is that it's practical to set up a secure subdomain with 301 redirects. It's not really possible to set up individual secure pages... and on some sites, it can get tricky to have the entire site seen as secure under one certificate.
That's because Security Certificates are issued per hostname, not per domain. You could buy a certificate for a secure subdomain... but for an entire domain, each hostname would have to be secure. If you tried to get an SSL certificate for the entire domain, you'd have to buy additional certificates for each subdomain, alias, etc. Otherwise, you'd risk running into SSL error messages all the time.
The security certificate warning message is browser related, so I can't imagine that the link rel canonical element would do what's needed to eliminate certificate problems. My interpretation of the link rel canonical element is that it's purely to tell search engines what your indexing preferences are. I doubt that the element would suffice to work with the certificates.
If your site is getting SSL error messages, it's likely that your certificate isn't set up correctly. Shared servers, as I remember, often have a shared certificate, which can lead to problems. Having an individual certificate and using it with a secure subdomain is really the best way to set things up.
While the above wording should be fairly close to correct, more server-literate hands than I will have to step in and clean up or enhance the technicalities of what I'm saying.