Hello R.,
I am sorry to refer to this, but I must, because I struggle with my 3yr old and sleep. Nanny 911 and Super Nanny. I did not search them out, but flipping thru the channel there they were and in almost every episode they address sleep issues. The key, they say and I found true, is consistency. The most difficult is the beginning, until your child knows you are serious and mean business and won't budge. The minute you budge you start all over, and I can say this with experience.
Your daughter will fall asleep by herself. It may take 3 hrs the first time and second time, but it will happen. There are many things I have tried and we are now at the following, which is not wehre I would like it, but it, ultimately, is a success:
I started with setting a routine. Before we got where we are now he would go to bed and I would pretty much wait by the door and put him to bed each time he got out of his bed and came to the door. In the beginning, I had to pull up a chair and wait by the door, and would spend close to 2 hrs there. I think only 3 times did I have to do that. Because we gave in once, I had to start over. I have held the door shut, he cried and I let him. Just kept putting him in bed. When he got upset enough, with me holding the door shut, I would open the door and ask, are you going to stay in bed, so far, once he says yes, he means it. They are resilient and manipulative. He is fine in the morning, forgives me, as if nothing happened, and we all got sleep. Now we are at this point: If no nap, the routine starts earlier. Warning that dinner is coming, so play, play, play. Dinner, bath, book, songs, prayer, music, lights out, door open. Routine really helps. And, if I miss a step, he reminds me. Sometimes it is 1 book or 1 song, sometimes 3, depending on how tired I know he is. I let him keep the books and a toy or two. The deal is door stays open, he keeps toys, but he stays in bed. He does not have to go to sleep, but stay in bed. As of today, he will always get out of bed once, I put him back and give warning, he will get out twice, I take all away, get out 3 times, I hold door shut (maybe 3 minutes) and he knows I mean business, I ask the question he says yes, and stays in bed. Sometimes he plays in bed 2 hrs, sometimes 15 minutes (like last night). Lately he has been going thru the diaper and bathroom deal, but he is potty training, that will most likely be a non issue for you. He did try the sippy cup thing, water and I finally caught on and said, before he goes to bed, drink water, none in bed.
A bit scattered and long winded, but hopefully you can get something from this. Bottom line, is don't give in, they will get it, but be consistent, and not with you staying in the room. If you can stand it, I have seen where you have a chair in the room and stay for a bit, DO NOT go into bed with your child, if they get out, put them back, and then leave. Each day you stay for shorter times, until you don't stay at all.you do not wait until they fall asleep, if they do, great, if not, they will learn to do so without you.
Best of luck.