My friend's daughter, HAD a friend like that.
They are not friends, anymore.
It was just too stressful for her daughter, and her.
Your Daughter is 6.
Certainly, I think you should be honest with her.
Just say, in a calm manner, that her being bossy and controlling... makes others not want to be around her.
If you walk on egg-shells around her and don't attempt to talk about it.... and just keep 'pretending' and giving her false reasons why she does not have friends, she will not learn. And she will not realize.
I have a sibling, that was like that too.
One day, my Dad, just TOLD her. That she is mean... and doesn't she KNOW by now??? She said she did. But she just wants everyone to do what she says. Oh well. So she didn't have friends, because of herself.
I think, your daughter or any child... just really needs to be told the truth. Pussy-footing around it, will not help them... improve nor teach them about people/social skills.
Again, I say this because your Daughter is 6.
If my daughter were 6 and having that problem... I WOULD tell her, honestly and calmly... and in a comforting way. But I would tell her. I would not lie to her and say its the other kids and not her, kind of thing.
Being isolated and pushed away as by others... is a real SIGN, that she has to improve.
I would just be honest with her.
If she does not learn this now.... she will have a hard time in each succeeding grade level. And then, what if she is teased etc., because of her inability to get along or because she is mean to others?
When my daughter was 6, she was in 1st grade. There was a girl in her class, that was REAL bossy and real Alpha, and not nice. My daughter knew right away, and just steered clear of her. Kids, know. My Daughter told me. I am always up front with my Daughter, about herself or how others may treat her. It serves to make them more articulate and able to "Discern" others.
all the best,
Susan