Hi ... I feel sorry for you. Sounds like you described my daughter... And having mild depression is for our family is putting it lightly. I suggest taking your daughter to an occupational therapast to test her for sensory integration disorder. I have also found that with my daughter communication increases the problem. We have adopted the following when there is a tantrum. We pick her up without talking to her or saying a word and take her to the bathroom where she has a special mat. She is screaming and kicking all the time. While she is on the mat - I sit away from her on the side of the bath and wait for the melt down to stop. I then pick her up and hold her while swaying her. Afterwards she is always completely exhausted (it lasts for +- 3 min) but better. I used to try to talk to her about what she felt but found that she is not able to word her feelings which would upset her again. Now I just leave it and show her that I will comfort her. That is for me dealing with tantrums in the short term but to get rid of it...
I would speak to your pediatrician about the problem and get an evaluation. most school districts can do an early intervention evaluation. i agree with you that something doesn't sound quite right. The sooner you get help, the sooner you will see improvements. There are several indicators in your description that lead me to believe it is more than attention seeking.
Try less communication when she throws the tantrums ignore some of it, and use the time out method, she is getting negative attention, focus on the positive side of her behavior, praise her when she does something good, children resond to flattery,dont we all, Omega 3 is good and try a Multiple Vitamin withB Complex and Vit C When she doesnt like you and her Mom talking she is trying to get your attention, do not give it when she demands but make sure she is getting plenty of Fun, games Reading and one to one time, outside activities.