A lot depends on how you feel about your relationship with your wife, but I'm going to assume here that because she's your wife, you clearly place no small importance on the relationship.
What this seems like is a classic example of someone being poly in principle - I believe your wife was 100% honest with you when she said she was ok with you being poly... and I also believe she's being 100% honest with you now in saying she wants you to be monogamous. When you first discussed the issue your role in her life and her emotional attachment to you were both very small, and it was easy for her to feel that poly made sense. Now you are very much closer to each other, and that can make people realize that what they are ok with in principle (that is on an intellectual level) causes them more emotional turmoil than they expected.
It doubtless feels to you that she's revoking her acceptance of something that you feel is a fundamental part of you, but I promise that's not the case. She's realizing that her needs are different, and she's communicating that to you very openly, even though it's doubtless very difficult for her to do so. If she has any relationship awareness at all (and I very much suspect she does) she knows that this may end your relationship - but she's willing to confront it anyway, instead of burying her feelings and trying to "make things work." Please try to appreciate her honesty and self-awareness - because of those traits, you have a chance to work through this by tackling it head on - not as the result of some drama that ensues only when someone reaches a breaking point. This makes it that much more likely that you can find something that will work for both of you.
One last warning though - as much as she might think she's ok with you having hook-ups, given how drastically she's limiting the scope of them, I really doubt she is. What I suspect is she's saying "I'm ok with you having other sex partners... but you can't care about them." Which of course, is unlikely to be true, even in the case of one night stands with strangers. Again I think it's coming from a feeling of wanting to compromise, and she probably really does think she'd be ok with it... but probably just like polyamory, she'd also find that the reality of it hits her harder than she expects, because of course it's unlikely that you'll have sex without any emotions what so ever.
I don't know what will work for you two, because I don't know what specific feelings you each have around monogamy and polyamory, and it's those underlying feelings that I suspect you have to address (Also, even if I did know, I'm not professionally qualified to deal with them) I would try to find a poly-friendly couples counselor sooner rather than later, as awkward or as unnecessary as it may seem. This is a major issue, and it's much better to be able to dig into it without having to untangle any related drama and resulting hurt feelings and resentment. You may find there is some way for both of you to get your emotional needs met, or you may not. But if you value amicable relations with your wife (and again, since you married this women, I very much assume you do!) I would take this seriously, don't rush to conclusions, and seek professional assistance.