You're actually completely right that poly is a bad fit for a relationship that needs repair. Work on yourselves first, get to a place where you're really strong, individually and together -- THEN you'll be in a much better position to withstand the often-rocky initial transition phase that happens in poly.
That said, why the acceptance -- even the suggestion, on your end -- of no-strings-attached sex with others, but the flipping-out reaction to the idea that emotions might get involved? Didn't it ever occur to you that some people, especially many women, either don't want to ever have sex with someone that they don't have feelings for, or can't have sex without feelings developing? Why is it ok to share the "legos" of her body but not the "legos" of her heart? What would you have done when she... or YOU (you never can predict these things)... developed feelings for a supposed-to-be-no-strings-attached sex partner if you and she had never talked about this in the first place? Feelings happen. Fact of life.
Poly IS more work than just swinging or having an open relationship or what have you. But that doesn't have to mean that you lose out. It comes down to whether or not you view love as a limited resource. Many, many people (me, my partners, the majority of the other long-time posters here, the Xeromag guy, others you can find numerous articles about) love more than one person without it lessening their feelings for anyone involved. It's really more a question of time management than anything, in the end, seeing as time is, in fact, a limited resource. But it's not like you'd try to stop her from having a hobby or a friendship that took the time that a boyfriend might, I assume?
So, yeah, my advice -- tell her you guys need to work on your relationship first (you will actually find plenty of support for this on the Xeromag site and in other poly writings), set a timeframe that you both can live with for re-opening the discussion (hopefully when she says that she doesn't think she can remain fidelitous, she doesn't mean that, like, she needs to put up a dating profile next week?), keep reading, and try to stay open-minded. Or dump her, your call. Cuz this probably isn't going to go away.
Me, 30ish bi female, been doing solo poly for roughly 5 years. Gia, Clay, and Pike, my partners. Davis, ex/friend/"it's complicated." Eric, Gia's husband. Bee, Gia and Eric's toddler.