Tough situation, and I fear that it is all too common.
The fact that you know yourself, and know that a poly/open relationship is not one for you and that you absolutely need monogamy is a very important piece of self-realisation. The fact that you have at least explored the idea and realised that it's not for you is admirable. I wish that more people had such clarity of thought.
Now, the remaining question is whether or not she is poly. The fact that she didn't think about having other relationships until yours hit trouble is an indicator to me that she is possibly not. For me it doesn't come and go, depending on how good my current relationships are. It's there, an intrinsic part of me.
The onus needs to be on her to work out what she wants, in the same way that it appears that you have done. Until she works that out, then things are going to be up on the air. If she decides that she is, indeed, poly and wants to have multiple (good!) relationships, then this is probably the end for you two - and that's a good thing, because otherwise you would just drift through life making each other unhappy. Who wants that?
If (as I suspect) she tends to be the type of person who will look for outside support when things go rough, then she needs to work out whether she wants to really put the work into the relationship that is necessary. This then is less of a poly discussion, but far more of a relationship dynamic in a monogamous sense, in which case, professional help will be best.
I also definitely agree that the worst thing that anyone can do when the core relationship is struggling, is to introduce another person - it doesn't fix anything, and usually makes things worse. In some ways it's similar to those couples who are really struggling and believe that having a baby will help magically mend their marriage.
"Listen, or your tongue will make you deaf." - Native American Proverb