Showing PDAs when you are out as a trio would be outing yourself as poly. Maybe you don't want to be out to all and sundry! Everyone on this planet who is of an alternative sexuality, be it gay, poly, kinky, whatever, has a right to come out only IF and WHEN they are ready.
If your gf wants to be seen as a poly trio and you don't, too bad for her. She doesn't get to choose for you. She can request public kisses and hand holding, you have the right to refuse. You're more private, less of an exhibitionist? Fine.
If you'd like to go out as a trio, but YOU get to "be the bf" and hold her hand, etc., ask your metamour if he'd mind if you go to be her hand holder now and then! Maybe he'd consider backing off on your 3way dates sometimes to give you a chance.
Love withers under constraint; its very essence is liberty. It is compatible neither with envy, jealousy or fear. It is there most pure, perfect and unlimited when its votaries live in confidence, equality and unreserve. -- Shelley
Mags (poly, F, 61) loving miss pixi (poly, F, 39) since January 2009, living together since 2013
"Master," (mono, 34), miss pixi's Dom for 3 years