I really recommend a discussion with at least your sweetie if not all three of you. There's no reason to be feeling like a second class citizen. Now, just wearing a ring I don't think should be a problem. DH never takes his off, I had to get him a special wedding ring that doesn't conduct electricity since he works with electronics daily! I know I feel weird if I dont' have something on that finger and the other ring finger since I fiddle with it all the time!
However, we've gone out and he's flirted with women and I see no need to make it KNOWN that he's 'mine'. If he chose to take the ring off when he went out as long as he was honest with people he was pursuing a relationship with, I wouldn't care. If it made his gf uncomfortable I'd be fine with it being off until she was more comfortable with a poly relationship. As long as it wasn't that she wanted to pretend he was single and just her man. That's just silly.
If anything I might get kicked out of a room while he was with a woman for teasing or making awww faces when he got affectionate. He's not huge on PDA so a hand holding is cute to me!
Me: 40 pansexual poly.
DH: My husband of 21 yrs and father of 3 teen girls.
DC: LDR of +9 years/former