So I am going to go against the crowd, and say something that isn't going to be popular, and people will probably flame me for and say I am projecting.
How you described your daughter's words and behavior. Very much reminds me od my sister and her behavior towards me. This is how she acted our entire childhood.
The individual attention, and we're a team aspect was not enough for my sister. I do not want to diagnos your daughter, but please consider therapy if you do not see improvements with the things being suggested in this thread.
Keep a close eye, my sister was very good at appearing to be playing kindly, but being very cruel..
Unfirtunately things like this wren't taken quite so seriously in the late 80s and 90s, so my sister has grown to be quite the terror in the family, and I have had to establish very firm boundaries. I think if things had been reconized earlier, and she had been able to receive helo beyond the advice of more attention, she could be in a better place and we could have a better relationship.
Again, I don't want diagnose your daughter. Just don't assume she'll grow out of it, and be open to her neededing more help that just one on one activities.