Well I think the first thing you need to do is fugure out everyone's goals for the relationships.
Does anyone have visions of long term committed investment? Kids, marraige, houses and the like or are the natures of these relationships more casual without much in the way of future expectations; seeing where things go and that sort of thing.
If there is an expectation for long term involvement then you've got a challenge on your hands. If it is more casual in nature then perhaps keeping them apart and having a DADT policy will work.
If your girlfriend hates this woman it may have more to do with her actually hating the concept of poly than the individual....that would be my guess. Your new interest is probably the physical manifestation of something she is really not wanting to cope with.
Playing the Game of Life with Monopoly rules.
Monogamy might just be in my genes
Poly Events All Over