has she been evaluated for autism?
I don't want to sound overly suspicious, but don't pooh-pooh the possibility of some kind of harmful or abusive situation when she is not in your care.
I agree with Annie, this is a concern and the first place to look would be her daycare situation.
I am curious, though, about your comment that you thought she was just spoiled because you work full time? I'm not sure I get what you're saying - "spoiled" children are considered ones who always get everything handed to them - I would think a child of a mother who works full time wouldn't be considered "spoiled".
Has she been checked by a doctor for any physical disorder or evidence of the need for a mental-health evaluation? When reading about reactions so extreme, I always wonder (failing any obvious medical evidence of a disorder) if a child who is being cared for by someone else is being harmed while in care, or harmed by someone the child is exposed to at home. If that is the case, now that she is 3, she should be old enough to tell you at least some of it, unless she has been conditioned to think it is just the way life is and nothing will happen if she does.