Hi M.,
i just want to let you know I understand what you are going through. I have stepsons that we do not have custody of, as well as my own almost 11 month old son.
But more so over that, I am from a broken hoome, with plenty of re-marrying and different groups of half-brothers and sisters about.
The important thing to remember about your step-daughter is that she is going to be emotional. Jus tlike any person, adult of child goes through a range of emotions brought on by rejection, jealousy, fear, ( I am sure that is a big one ) etc.
being 6 she can't hide her emotions like an adult, or be as reasonable.
Alot of kids get tough breaks, and are labeled because of it. Children are notorious for change and any given behavior will dry up and blow away given time. Patience is sometimes hard to come by, especially when you are taking on so many challenging roles as you are.
you are right to giver her plenty of love, and some space too. just be strong for her and your family, and sometimes try to remember what it felt like to be 6, or maybe a time in your life when your place seemed very scary or uncertain.
If it were me, I would try to find another outlet for her besides family and school. Maybe she would improve in her social skills, and behaviors if she had another group to fit into that had a good peer structure. Like dance or gymnastics, girl scouts, or even Sunday school.
whatever you do, don't give up on her. And be cautious of seeking help. If you really need outside help consider a situation possibly less ostracising for her than therapy. I am not a church person, but I know as a child I felt filled with love going to church with my Gramma..
Good luck!