I suppose you could say I'm the hinge in a couple of V's. Gia is dating me and Davis is dating me and Clay is dating me and none of them are dating each other.
One of partners, Davis, isn't seeing anyone else. While with Gia and Clay I feel perfectly comfortable mentioning my other partners in casual conversation, I find myself censoring myself now and then with Davis. I try not to do things like your example -- "I am going to see my parents" instead of a simple "we are going to see my parents".
-- but I do still sometimes worry that thinking of my other partners will upset him, and so I still occasionally edit myself without really thinking about it.
The difference is that Davis doesn't WANT to know about my other partners if it's not relevant to him. He's not trying to pretend they don't exist, he just doesn't much care. If he was actively asking for info, or to hang with them, I would be all about it. Why would I try to hide the people that matter most to me, when instead I could have everyone I care about together and bask in their combined attention? But then, I'm an extrovert like that.
The major players. Me, 30ish bi female. Gia, girlfriend of 4+ years. Clay, boyfriend/dom. Davis, ex/friend/"it's complicated." Eddie, roommate & fwb.
The supporting cast. Eric, Gia's husband. Bee, Gia and Eric's toddler. Dexter, Gia's lover. Helen, Eric's lover. Izzy and Nikki, Clay's partners. Liam, Eddie's husband.