yeah, the sitemap is cached by the runtime, you have 2 different web sites that point to the same set of files and database, the one that adds or removes a page can clear its own cache but it can't clear the cache of the other site, so the change won't be seen on the other site until its own cache is cleared or expires

bottom line: shared ssl is problematic for many reasons, we think it is a very bad solution, we don't support it and we recommend don't use it.

my best advice for you is get a real ssl certificate for your own domain and don't try to use shared ssl