Originally Posted by
lillamy 
"it was amazing to see -- when you set a firm boundary, she calmed down. It was as if she was looking for that boundary."
This is has been a lot like my experience too not so much with my own daughter but one of my best friend's little girls. Her husband is a terrible A who relapsed about 6 yrs ago & has been in an intense cycle especially over the last 2-3 years. The 5-yr old RULES at their house because to accomodate for the addiction they both allow her too much freedom (& he's never been an involved parent). It's just awful to watch, she melts down over everything & has this expectation that everything in life is negotiable.
WTBH - I agree with the advice you already gotten here & it sounds like you've got great awareness about the situation. You mentioned talking them through the thought & correcting it, have you also been proactive by playing to their strengths as well? Like if ... {I'm absolutely improvising on these scenerios - I don't know anything about your girls} ...D4 is great at/loves art, set up an afternoon where she can dive into it with all her supplies & praise the holy heck out of all of her efforts? If D6 loves her pet cat maybe she's old enough to have the chore of feeding it every day & then you can sing her praises on a regular basis when she accomplishes that task daily?
And, even though I'm starting to sound like a broken record.... I would highly recommend reading "Perfect Daughters" from the point of view of helping them avoid developing deeper codie behavior. ((((HUGS))))