I have trouble with this as well. It's not shame as much as it is not liking the fact that when we share PDA in public, it becomes "a thing" in the public's eye, rather than it just being nothing to look at.
If it's just the two of us, it barely gets any recognition, which is nice - I'm not looking to hold his hand in order to get attention or "aww, cute" comments.
When it's the three of us, I feel like it's a circus (although I know it's mostly in my own head), and I don't like the attention it receives. It makes the nature of the relationship more important, somehow, than the relationship itself, and that drives me crazy. I've also been burned by the judgment of sharing PDAs around people I know ("You deserve better. He's being disrespectful") so I'm also sensitive to that, especially if I'm around people whose opinions may actually negatively impact me (coworkers, family, and the like).
For reference, I've been in this relationship for 2+ years now, and this isn't going away for me any time soon.
I don't feel I'm "not cut out for this relationship" but this aspect of it isn't for me, and I do pull back physically when we're all together. P and M1 have sort of accepted it, and try to not make me uncomfortable when we're all out, which is nice, but to be honest, I'm not limiting their PDAs, just pulling back on mine. He and I have enough "together time" as a couple where I don't feel I'm missing out on anything.
No answer for you, but some empathy, if that helps any.
Mono. Divorced, two kids (DanceGirl, 15; and PokéGirl, 12), two cats, one house, many projects.
My partner. Poly.
Chops' other nesting partner, Poly. Also in a relationship with Shaggy
Chops' other other partner (heh). Married, Poly.
Poly, in a relationship with Xena
External mono/poly blog: From Baltic to Boardwalk