Hi S. - I think my opinion may be a little different. I have two children one who will be 4 tomorrow and the other is 21 months. I have worked part time since becoming a mom, but it was mainly third shift so as far as the kids were concerned I was a stay at home mom. For the past year I have worked from home so again they are with me constantly. My daughter who will be 4 tomorrow started going through seperation anxiety at about one year of age. We only noticed this because we go to church consistently and it was the only time she was not with me. The min we walked in the door to the church she would start screaming! Acouple of times I was even asked to come get her and to keep her throughout the service because she would not stop screaming and she was making the other kids scream as well. So long story short my husband stayed home with her through this time and I went alone. This went on for about a year. When she was two we took her back and it took about a month of taking her every weekend before she finally calmed down enough to stay through an entire service now two years later she loves church and preschool, she is in her second year of preschool now.
When my son turned one, he began having the exact same issue. So we went back to daddy stays at home while mommy and DD went to church. However, my daughters preschool teacher from last year sat me down and told me I was not doing anyone any good by keeping him home. He was in no way being harmed by being made to stay in class and if I would just commit to brining him every week to the same service (we have four servies) he would be just fine and would begin to calm down enough to stay through the service and eventually get to the point of wanting to go! And sure enough after one month of taking him every Sunday to the same serice he now runs into the room all by himself and doesn't look back to wave goodbye or blow me a kiss...which strangley enough I am ok with. My point is that if your daughter has NEVER been away from you this is going to be REALLY hard and very taxing on you both. But I highly doubt it means she is not ready. And at three it may take her longer to get over her seperation anxiety then it did my children who both got over it much earlier.
I would suggest that she be moved to a different classroom. It will not help to have you there. Talk to the teachers and find the one who is willing to be calm and patient and understanding. I absolutely LOVE the teachers in our preschool because I have watched them with the kids and they are ever so patient and caring and always reassure the parent. If you run into a teacher who wants you to remove your daughter, find another teacher! Preschool is really very benifical and it may take some time, but your daughter will be okay. You are not harming her, it honestly will hurt you more than it will hurt her.
Good luck! I know this is not an easy time, but you will make it through!