What does your existing redirect look like? mod_alias or mod_rewrite?
Other questions: Are some pages reachable by both http and https, or are they mutually exclusive? You said htaccess, which I assume means shared hosting. Does the new domain live in the same userspace, or under the same primary domain, as the old one? That is: will it pass through the same htaccess?
Does the redirect for https pages simply not take place, or does something else happen?