It sounds like you and your lady are entering into a deeper relationship than you or her had before. She seems to be used to the serial poly style where by she has many lovers, none of them particularly deep, but loving nontheless. If you and her want to establish something more deep then, the "anything goes," "we have our freedom" thing doesn't work in my opinion.
Firm boundaries need to be set. Those can be discussed and moved around but they need to be made to protect your hearts and feelings. It simply creates respect for each other and will deepen your relationship to no end. Not to mention the freedom that comes with that kind of commitment.
Interesting you would think this ultimatum talk, hmmmm?
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