Oh Jesus. I just realized I have been using the secondary title plugin, not this WP subtitle one.
Sorry for wasting your time!
I am quite confused by your question and answer. But I will try my best to answer and understand.
You asked: Are you appending the the subtitle to the title including the HTML via a filter?
I don’t know anything about filters. In fact, this is the first time I have heard of them. But, I just deleted the facebook open graph plugin and that eliminated the problem with the subtitle.
I am still have major problems with my featured image/getting images onto facebook.. But that’s a different story.