Your relationship is dysfunctional. All the snooping, mistrust, lies, BS is not normal or healthy. And it would be very selfish of you to expect fidelity from her while you do what you want. Honestly I get the impression you are the problem-you started all this-made her feel insecure. She lost trust in you and leant on someone else for emotional support. Here we are only getting your side of the story but if you read in between the lines with some of your additional info- I get the impression your controlling, abusive and untrustworthy. You have crushed her confidence so bad-that shes willing to do or say anything to keep you.
This relationship is co-dependant. Honestly I have been in a 6year relationship and I have never had any of these issues with my bf. We dont fight about sex or trust etc.. your not compatible.
If you want a polygamous relationship-find a woman who wants the same and who will also see other people. If its not equal-then its abusive
"Don't ask a question if you can't handle the answer".