I've been married for 19 years and though I love and get along fine with my wife in most ways have felt cramped, uncomfortable and even depressed to an extent trying to fit into the mono stereotype ... it got to the point where it was almost a continual ache to find some outside femanine company to enjoy (even if it not specifically sexually, at least as boyfriend/girlfriend with sexual tension/overtones).
I don't know how strongly your feelings are, but if you left a previous marriage over the issue then it seems you're likely in the same boat - I've felt better all around for almost half a year now simply by letting myself flirt around a bit with other women and me and many people I know have noticed the difference.
I'm just saying all that because it appears you're similar though you've recognized it earlier ... though I can tell you from the long-term perspective that it's not something that appears to go away or let up.
If you were upfront from the beginning with her, then she's likely made the mistake of not having been upfront with her feelings (apparently she's not very honest with her other boyfriend either).
You don't necessarily need to leave her, but I don't think trying to cater to a double standard is going to work out well and you should continue to be what you're most comfortable with. (She sounds a bit possessive and manipulative - that's a combo I've tried to avoid in women I've dated). If she truly can't accept it and leaves, well that's her loss. If she's willing to accept it and deal with it over time, then likely things can get better, though I'd assume it more likely that with the state of things between the two of you, you'll probably find someone more accepting of you and better in terms of a long term relationship.
Yes, sometimes emotions are frustratingly stubborn LOL
... can't always "talk sense" to the heart, but from personal experience, if you make emotional appeals to yourself instead of trying to purely use logic ... feel what you want, and the emotions can line up better with the logic. When you can find a way to line up emotional desires with the intelligence to find a solution to satisfy them, life can be great
Good luck, David.