I know that alot of folks here won't agree with me, but I consider myself an AP parent and I had exactly the same situation as you.
My dd was 25 mos. when ds came along. Claudia was sleeping in her own bed in her own room, but she had never been able to go to sleep by herself. Like you I was spending 2 hours getting her to sleep usually by laying down beside her or sitting in a rocker beside her bed, but I COULD NOT leave the room until she was absolutely asleep or else she would scream. When my dh started working late and it was just me in the evening with the kids I decided that something had to change.
For a few days I prepared dd by telling her that it was time for her to be a big girl and go to sleep by herself. We read books about kids going to sleep by themselves. And finally one night I tucked her into bed, said goodnight and walked out the door. Of course there was much wailing and many times that I came back in to talk to her and get her settled down. I guess that this is essentially a CIO method, but I felt that I had no choice. After about a week of this, one night I put Claudia in bed and she smiled, said goodnight and rolled over and went to sleep! It's been more or less like that ever since. While we never had a family bed, I think that this can be the same for you.
There was a thread a while back along the lines of "are some kids easier to AP than others?" I think that this can be true. With my ds, from the time he was 9 months old I have been able to put him down awake and he will roll over and fall asleep by himself. I never had to go through all the drama that Claudia required. I think that they are just very different kids.
With your daughter you may be able to get her to sleep with you sitting on the bed instead of laying beside her.