Technically yes, but probably only on the "regular" domain. Your deity provides access too certain subdomains, and if you're using Separatist to grab a domain they don't grant, it's rather unlikely they have access to one of its subdomain.
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I'm not sure why a Cleric wouldn't be able to take a subdomain with Forbidden Rites. The entire point of Forbidden Rites is that you're allowed to break the rules regarding deities and domains, and 'subdomain' is a legal substitution for a regular domain in all other contexts.
I suppose if you want a really lawyery answer:
Subdomains are treated as equivalent to their Associated Domain for any effect or prerequisite based on domains
The only prerequisite for Forbidden Rites is "a second domain that is not on her deity's domain list", and subdomain = domain for all prerequisites.
That's a very reasonable take on it. I'd ask your GM and see if he cares.