On our homepage, when you visit the site over a normal http request, the site loads very very quickly (less than a second). I am sitting right next to the web server. When you visit the site over https it takes 10-20 seconds to load.

Here are a few other symptoms. If you look at the certificate in IE, under the Certificate Path, the certificate status is:

This CA Root certificate is not trusted because it is not in the Trusted Root Certificate Authorities store.

In FireFox, when you browse using https / ssl you are presented with this message:

Security Error: Domain Name Mismatch
You have attempted to establish a connection with ".b.". However, the security certificate presented belongs to ".a.". It is possible, though unlikely, that someone may be trying to intercept your communication with this web site.
...

Any ideas?