You really should have been playing this different all along. You should have been having threesomes with random girls together from the get go. Now you're stuck.

The threesome needs to be spontaneous. There's no way your girlfriend is gonna plan that shit with you if she gets jealous over you talking to another girl.

But you also don't want to hurt your girlfriends feelings by ignoring her and not communicating properly. The car ride home after an awkward threesome is something I wish upon only my worst enemies.

My suggestion to you would be bring her to a strip club with you. Feel things out from there.