My 6 yr old daughter behaves appallingly, she moans, whines & strops out whenever asked to do something?

that she doesn't want to do. She throws monumental tantrums, where she will scream, shout, hit out, bang doors, throw toys etc. She just hardly ever seems to be happy. At school she appears to be well behaved apart from not listening to instructions properly, not sitting still and finding it hard to concentrate. Yet at home she can be extremely destructive and it's getting me down. She lives with both her parents and her 2 yr old brother. I have suffered some depression, anxiety and low self esteem over the years, and there is no doubt in my mind that some of this will have had some effect, but if anything, my health has improved enormously over the past couple of years. She is a very sensitive little girl who tends to take life very seriously. I am desperate to help her out of whatever she is going through. I have talked to my health visitor several times, who has suggested a number of things that I have tried, like reward charts, ignoring the tantrums (extremely difficult) praising positive behaviour...I'm ready to run away, is there anyone out there who can give me some advice, or reassurance?