"Unicorn" doesn't simply mean someone who dates couples. It means someone who doesn't have their own personhood and exists only to fill a role in a relationship -- not as a human being with thoughts and feelings, but as a placeholder.
If you were a real unicorn, you would enjoy being tossed around and having your emotions played with and the on-again-off-again. You would never have grown closer to one of the couple, because unicorns always love both people equally. You would wait at their beck and call whenever they have couple-issues to work out, and then you would rush back when they show the slightest interest in allowing you. And you certainly wouldn't have alone time with either of the partners, because unicorns only have sex and intimacy in threesomes.
That's why it's called "unicorn" and not some other, non-imaginary creature.
Cut them loose. They're not ready for this. They practice avoidance rather than confronting their problems. A break from a relationship can be useful to see if you really want to be together, not as a constant coping mechanism to avoid dealing with problems when they get to be overwhelming.
Labels are sticky and I hate the glue they leave behind.