I think when Olivia crossed over while in Walter's office, fauxlivia crossed into our universe. And that's where they've each remained since. So fauxlivia is actually from our universe and Olivia is actually from the alternate universe. That's why Peter fell for fauxlivia so hard and fast — she was the one he'd connected with as a child in our universe, the one he sat with in the white tulip patch.
I'm not sure yet what this means in terms of the love angle [point finger in mouth to signify nausea here]. I'd think it means Peter will choose who we know as fauxlivia, but I really don't fucking care. The more important thing is the baby [point finger in mouth to signify nausea here]. The baby is what will save the universes because it's a half-breed — created from Peter (who's from the alt universe) and "fauxlivia" (who's from our universe).
And that's as far as I've gotten on this.
ETA: I forgot to mention something that's bugging me. Why didn't Peter know who Olivia Dunham was the first time he met her in the pilot? In tonight's episode, Walter told young Peter her full name. Peter looked through her sketchbook and spent time with her in the tulip patch and it seemed pretty significant to him. Likewise, why didn't Olivia remember Walter when she first met him in the pilot episode? Am I forgetting something from episodes past about their memories being blocked?
ETA 2: In rewatching those last few scenes again, I realized I was confused about which universe we were in. I thought it was Olivia in Walter's office in our universe, but that scene actually started in the alternate universe and ended in ours. This doesn't mess up my theory at all and I'm still convinced about the Olivias swapping (though I'm worried the Olivias may have swapped a couple times, in which case we might not even know who's who). I need to rewatch this whole episode again. And this is the first episode in a very long time I've cared enough to rewatch :)