When I was dating my now husband, I moved to the apartment complex he lived in and directly across the parking lot from him (so I looked out my apartment's sliding glass patio door over to his apartment's sliding glass patio door). I "lived" with him though and noticed a stray cat I started feeding, against his wishes :-) out on his patio. It was getting late in the year, October/November and started to get colder so I had a wooden beer case I outfitted with towels and made him a warm nest in it for him to sleep in. My husband/boyfriend was adamant about not wanting the cat/don't bring him in my apartment, etc.!

The day came when it was getting too cold and I couldn't stand the idea of the cat being exposed to the cold so I had to think in terms, "cat or my true love?" I chose the cat and that evening told my boyfriend I was taking him in/keeping him (in my apartment) taking him to the vets to be checked out, etc. I steeled myself as I thought I was wrecking my life/happiness. My husband was fine/as long as I kept the cat in my apartment, no problem! :-) However, we moved within the year to a house and, you guessed it, the cat came with us and was an "outdoor" cat and "ours" for the next 15+ years. My husband came to care for the cat over time and now we have two :-)

Maybe you can get a larger place or change situations so she and the cat aren't as "together"? I would have a literal heart-to-heart conversation with her and explain to her in actual words that you love/care for the cat and you love/care for her (differently, there's no "competition" it's like loving your mother and girlfriend at the same time :-) so she understands that a lot of the "choice" is her responsibility, not yours. You have chosen the cat AND her and it's her responsibility to decide what she wants to do about that. But like I say, if your girlfriend moved in with you, into your place, maybe you all can go out and find "our" place that is big enough, has a way, to get the cat out of her space some of the time (where she has her own room the cat isn't allowed in, that sort of thing)?

If that's not possible, I'd try to exclude the cat from some areas of the place you are now, the bedroom, for example, and/or maybe restrict it for awhile each day in rooms you aren't in together, etc.