It doesn't sound like she doesn't want to sleep. It sounds like she doesn't want to sleep without you, which, in spite of all our Americanisms about how babies and children "should" be, makes perfect sense from the perspective of human development and a three year old. Most cultures in the world do not consider it important to have a young child sleep apart in a separate room, and it is certainly not necessary for her to do so if you feel comfortable with her.
The "family bed" is a very snuggly, warm place, and it is a way to give your little girl the important self-confidence and feeling of safety that will allow her to eventually move to sleeping on her own, or maybe with her younger sister when she is older, too. It's also, by the way, pretty wonderful for you--those snuggles and deep connection with your little girl can go a long way later in life! I'm speaking as the mother of three daughters, one who is 19 and on her own now, one who is 15 and jealously guards her own room, and one who is 10 and has just recently stopped coming in our room occasionally, but who has mostly slept in her own room since she was about 5-6, with phases of wanting us more and phases of wanting to be on her own. I promise, eventually they DO grow out of it, but if you let them do it on their own terms, there will be a stronger sense of self when they do, and they will NOT go into their teens wanting to sleep in your bed! ;)
As far as the monster thing goes--many here have mentioned "monster spray". We did it a little differently ;). I garden and have always told my daughters fairy stories. When my first daughter, at age 4, became certain there were monsters in her room, I took a peacock feather she had in her room, and walked out to the flower garden with it. I then came in and told her I had asked a few of the fairies to come in on the feather and help keep monsters out. Monsters are VERY afraid of fairies! We used that feather as a "monster sweeper" and would sweep all the corners and under her bed.
Went back and forth with all of them between them sleeping with us and in their own rooms.