By all means, if you want to personally claim the label "unicorn" as meaning "I date couples," then that's your privilege. But privilege comes with responsibility. In this case, it's the responsibility to make it clear to your readers that you are deliberately reclaiming the label, and not merely misunderstanding it.
People use the label "unicorn" all the time to connote a woman who dates both members of a hetero couple. I do not believe anyone truly expects said woman to be mythically perfect: equally attracted to both of the couple, secondary to the hetero couple, etc.. It is just easier to say "I'm a unicorn" than to say "I'm a woman involved with both members of a heterosexual couple who were already together when I got involved."
I disagree that the poster has any responsibility to "reclaim the label." We all know what she means by "unicorn," and if the reader is attaching all kinds of baggage to the term, that's the reader's issue. I just took it as the poster is a female dating a couple, and her relationship to them is as unique as anyone's relationship to anyone. Obviously, there is a need for a word to describe such a person, and unless someone can come up with a better or more succinct term, unicorn it is.