She is cheating and you are not able to share and you are going to move to be near her.... wow! I don't know where to start.
From my own experience. I make a point of reminding myself
-don't date cheaters
-don't encourage cheating
-if you can't share, date separately
-don't move people in a state of NRE
So this woman came to visit you and didn't tell her partner and you think that is not only okay but encouraged it by having her stay with you. This person is being lied to. He (?) thinks he is in a monogamous relationship with a woman that is faithful and committed to him. If you were in his shoes, how would this make you feel? If you were standing beside him at the bank and new that you had touched his woman without his knowledge or consent, how would you feel? Do you not think she could also cheat on the two of you? Where is her integrity? Where is her back bone to stand up for herself and begin making moves to better her life by addressing the issues they have or leaving if she is not able? Where is your integrity in this? You are as much a part of this as she is. I suggest you do a tag search on "cheating" and see how cheating has effected people in their lives, poly or otherwise. There is a lot of info on here that might help.
If you can't share, then why are you dating the same people? This is not essential to poly relationships I don't think... in fact it seems to work better to become independent and find ones own loves. Sharing time together, sharing stories of what you do with your life and sharing a future together in poly is where it is at for me. Having lived this for a good long while; not making rules about sharing lovers...if that comes, great... but is not ideal.
Triads such as the ones you describe making rules about for your poly life, seems to last until the NRE is over. Then when it becomes impossible to live ones life doing everything together it becomes a matter of who loves who more and who doesn't really want to have sex with who and who is spending more time with who and ... petty stuff ya know? At least of the relationships I have known that last over a year, sometimes less, if this isn't worked out or at least considered as it goes along, then its usually done. Maybe that doesn't matter to you though and under a year is enough... doesn't sound like it if you are moving close to each other.
That leads me to another thing... moving. It seems to work better to save all that until after the NRE is over. Being drunk on puppy love is fun, but not a great time to make life changing decisions. Just cause he knows her and has a history doesn't mean that this will be the same with you in the picture. it will be different. Three is different than two. Why not see what those differences are before making huge changes to your life.
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