(First: I had difficulty reading your OP due to the density of the text. Distinct paragraphs breaks and some white space make posts much easier on eyes, and therefore more likely to be read and draw responses.)
Next, my advice for your predicament:
If you are cheating, stop it now. You cannot build an honest, open, loving and respectful relationship on a foundation of deceit.
Turn your attention to yourself. Figure out why you chose to cheat. Then work on those problems. Encourage your current partner to do the same, recognizing that his issues are fully his responsibility.
When you have worked through your issues, and are ready to give and receive love in an an open, honest, respectful way, look for a partner who is also interested in this kind of relationship. Perhaps your current boyfriend will have worked through his issues. Perhaps not. Either way you will be better off than you are now.
There will be other polyfolk here who will disagree with me, and give you advice on how to salvage your current situation. With much respect to them and to you, my experience is that cheating taints relationships permanently. If you reveal your affair to his girlfriend, how will she ever trust him or you fully, knowing that for a year the two of you lied to her? There would always be that gnawing doubt in her mind, and the two of you could never FULLY regain her trust having betrayed it so deeply and for so long. Better to address the issues in yourself that lead to these bad choices, wipe the slate clean, and move forward in a healthy, loving manner.
If you have NOT cheated, the opportunity still exists for open, honest and loving communication between the three of you. He should take the lead and introduce the possibility to her, as it will be a HUGE change to their relationship. The two of you should be prepared to approach the discussion in a manner that demonstrates respect and love for everyone involved (not just the three of you, but also the children and anyone else impacted). Continue demonstrating that love and respect whatever her reaction may be, and wherever the situation goes from that point.
Best of luck to all of you. May your lives be filled with joy, peace and love.