Tough situation. I would say that it is best to just end it or take some time apart, but I am not sure it would change anything. Resentment can enter the picture...if you allow it to.
I am in a mono relationship despite how once I structured relationships in the past. My other relationship ended in March. Am I happy with the new structure? Yes. Do I feel like I was forced to do anything? No, because I suggested and willingly chose to not be able to enter another relationship without losing everything. (A good old fashioned cheating-like clause.) The difference with me is I am on the asexual spectrum. I am a demi, and I do not feel attraction to anyone but people I have established trust and developed a special bond with over time. In 18 years of practising poly, it has happened 5 times and only once after I met my DH. The last time a connection happened? 13 years ago, so the odds of it happening again are virtually non-existent.
I would definitely say take some more time to talk, learn about poly, and see if there is a way for it to work. Mono/poly relationships can work if done the right way. Most couples do NOT just jump in to it, and when they do, sometimes it bombs because they are not prepared and shit just goes wrong. Just because YOU have been feeling this way for 10 years does not mean she knew, suspected it, or ever pictured poly being part of her relationship with you, so you have to strike a balance. It is hard for some people to imagine their partners loving someone else and doing the things they have been doing with them for x years. Honestly? If you felt bad about two weeks and felt like it was cheating, then, you have some more work to do internally. Realising one is poly and actually taking steps toward it...not the same thing by any stretch, and neither comes overnight. It is not, "OMG. I just discovered this mystical and fantastical thing called poly. Now, I need to go find someone to give this over abundance of love to." *sprinkle pixie dust here* It is like the latest dieting trend. Would people just dive head first without doing adequate research and learning about the side effects--or in the case of poly--ramifications? Fat chance. How long ago did you and your girlfriend start talking about this? How long from that time did you start the relationship with the friend?
Have you ever asked why she specifically has a problem with you sharing your time and probably heart with another woman? Is it the fear that you will stop loving her or that she/your relationship will somehow get neglected? I tend to believe there is a root. I am asking because usually the fear is irrational and can be allayed with time. Might I suggest seeking a poly-friendly therapist? Fair warning: they are not the easiest to find, but it helps having that unbiased third party to help with the fluidity of communication.
The others have offered pretty good advice, so I hope it works out for you.
Ry - Me. Panromantic demisexual with a history of polyamorist tendencies. Married to...
Matt (Hubby) - The once distant stranger that I complement beautifully. DH of 12 years and father of our (3.5) children.