What's wrong with our daughter?

well you mentioned that she had sad and troubling events in her past, maybe these are bad enough to make her act like this. it could be that she is just looking for attention, like when she exhales loudly and claims nothing is wrong, when she lashes out at others for nothing or the dramatic change into the "gothic culture". part of this might just be teen angst, like when she is asked to do simple chores and complains. i would suggest that you confront her about her behavior. be kind and understanding to what she says but also be strict and don't let her drop the subject or push you away. she might need to see a counselor to just discuss her problems so she doesn't take it out on everybody.