The initial waking up sounds like night terrors. We just went through this with my son, who is also 1.
The thing with NTs is that you need to wake them up. It can look like they are awake: eyes open, and so on, but they are in fact asleep. Turn the lights on, be loud, etc. The only thing that really woke my son up was a cold washcloth on his face. (People who responded to my request about NTs a few weeks ago also suggested going outside with him, into the cold air, but we never had to do that.)
NTs decrease if you leave some sort of constant noise running in their room: a continuous CD, a noise machine, whatever. We leave a small fan running on high in his room, and he has only had 2 NTs since we started doing that. For awhile, he was having them almost nightly.
Your daughter staying awake and then subsequent wakings (unrelated to NTs) are likely due to her sleep schedule being "off", and she's now programmed to be awake for part of the night. We also went through that phase w/my son, where he was up for like 3-4 hours in the middle of the night, wide awake and wanting to play. My husband indulged him, but I finally put my foot down. We were all exhausted and it had to stop. When he would wake up (unrelated to NTs) we would keep the lights off, give him something to drink, change his diaper, and then put him back to bed. He did cry the first 2 nights, then after that, he started going right back to sleep.
You should never, as a parent, do anything that makes you feel uncomfortable, but I wanted to share that crying it out did work for us, and rather quickly. Crying it out does not involve just shutting the door and walking away. (I read stories of babies being left to cry until they vomit, and I shudder!) You have to be attune to your child's cries, and go back in if they need you. I know my son's different cries, and I can tell when going back in will only rouse him, and when it will soothe him.
If you are OK with her crying for 5 minutes at a time, perhaps you could try letting her cry for 5 minutes, going in and soothing her, and keep repeating that until she does finally go to sleep. You would not be letting her cry endlessly, but she would be getting the message that it was bedtime.