Don't do swinging if you can't handle poly, feelings may well develop where it was supposed to be "just" sex, and then you're right back where you were.
I am NOT trying to make you feel guilty, but I do hope that ultimately things can work out with her and the man in the other couple if their feelings for each other persist through the break. If you can overcome your difficulties with it, there's no reason that your relationship or lack thereof with the woman of the couple should have to play into it at all. I think the time spent outside of the situation and the counseling will help immensely either way.
Me, 30ish bi female, been doing solo poly for roughly 5 years. Gia, Clay, and Pike, my partners. Davis, ex/friend/"it's complicated." Eric, Gia's husband. Bee, Gia and Eric's toddler.