I would agree with the advice to go to counseling... this is somewhat like the situation with my older sister and me - and if not dealt with, it only gets worse. In our case, it was special needs due to disability, not differing LOG - that fueled her jealousy - and her temperament tended to have her do all those negative behavior - yell, slam doors, sulk etc.
Also - make sure you know the peer groups your DD hangs out with. That was one of my parents' regrets - they did not move her out of what ultimately turned out to have been possibly toxic school environment, so her friends only fueled her negative behavior and anger.
My older sister's jealousy even got so bad that when she was 11 and my parents could only take my younger sister on a trip - my dad traveled a lot for work - the 11 year was determined to scare her 3 year old sister to the point that she refused to go to the water at the beach simply because she could not go on the trip.
She has a lot of issues stemming from all that today as an adult which is why we have no contact with her (thank goodness - I have no idea how she would have reacted if she ever got a whiff of the LOG of our kids but it would be ugly). She has not been able to develop the maturity and perspective that one tends to expect with adulthood so the rivalry is stronger than ever - but only in her mind since I don't bother talking to her nor really care that she is out of my life after the constant strife she dragged me through for so many years.
