I don't think that this type of certificate will do what you are trying to do. It seems to be geared more towards mail servers. It seems that the 'issued to' part of the cert, that a web browser compared with the domain name used in the URL of the page you are on, can still only be for one domain, see:
http://help.godaddy.com/topic/599/article/3908
'UC Certificates are compatible with shared hosting; however, the site seal and certificate "Issued To" will only be for the primary domain.'
So if you are trying to use this cert for both
https://domainone.com and
https://domaintwo.com, it probably will not work, or at least the browser will likely present a domain name security warning to the shopper if these are not the main domain in the cert.
A different kind of cert for multiple domains is a wildcard cert, it can be used by multiple sites on the same IP address, but a wildcard cert can only be used on subdomains of the domain that the wildcard cert is issued to, so you would have to assign additional hostnames to each site to use it, i.e. domain1.yourdomain.com and domain2.yourdomain.com. Wildcard certs are generally expensive, so you would probably have to have a lot of sites that would need to use it before it would be worth it to purchase on of these.
http://help.godaddy.com/article/857
Another solution could be to purchase one cert for your hosting company's domain (assuming it is on the same server) and create some VirtualDirectories (Aliases and ScriptAliases on UNIX/Linux server) under that site for each ShopSite site's ss, sc, and home directories. Then you can configure the secure URLs as (for example):
https://yourdomain.com/theirdomain-sc
https://yourdomain.com/theirdomain
https://yourdomain.com/theirdomain-ss
https://yourdomain.com/theirdomain-shopsite-images
But if your clients don't like having anything other than their domain in the URL when going secure, then I don't see any way around getting a unique IP address for that site and purchasing an individual SSL cert for that site's domain.
-Loren