Just so we're all using the same terminology, "unicorn" typically refers to a woman who will join a MF couple, and love them both equally and join their relationship and they'll all become one big happy family.
Reading between the lines, it sounds like you wanted a woman to come share regular casual sex with you and your partner, but not form an emotional bond? We don't usually think of that as a unicorn... I'm not sure we really have a word for it, actually. Sex toy? It's probably easier to find a woman to be a regular sex partner, with no romantic strings attached, than it is be to find a woman who can fall in love equally with two people, and with whom both people can fall equally in love. That's why we call them unicorns.
And so now, I'm also confused about the nature of this emotional attachment. You say you're friends first, sex partners second... but where does loving, romantic partners fit into that? Off the table completely? Third after sex? Between friends and sex?
“As I am sure any cat owner will be able to tell you,
someone else putting you in a box is entirely different
from getting into a box yourself.” —bisexualbaker