Meeting your new gf's longtime partner is just par for the course in poly land. Even tho you all claim to be mono, this is a poly situation. You're living with your former lover/best friend of many years. You've got a LTR of over 2 years duration with a 2nd person. Your gf has a new gf of 2 months. This is a poly tangle.
Of course the new gf is afraid to meet you. She imagines you as a monster, and you imagine her as one. Actually meeting will show you both you're just normal people with similar feelings. Stick to your guns. If the new gf is so scared to meet you that she refuses... well, then, she's showing lack of character that should show your longtime gf something about her, that might decrease the NRE.
Your gf is afraid breaking up with new girl will hurt her? Well, obviously new gf is already having unpleasant feelings of jealousy and fear even without being dumped. I don't know what she was thinking, falling for an allegedly mono person already in a LTR. She made the choice to fall for her, now she's gotta face reality and "pay the piper" by meeting you. Least she can do, IMO. Sack up, as they say!
I am glad your gf is refusing to see new gf alone until new gf meets you.
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
In a newish relationship with Steve, (34, poly)
"Master," (mono, 34), miss pixi's Dom for 3 years