I'm sorry, I guess I don't see in the original post where the little girl was held accountable. OP states:
"She knew she did something wrong because she was sitting in the corner with her head down. I quietly brought her upstairs to her bed, and talked to her about how it was very bad to bite a baby, how much she hurt her, etc. At firat she was upset and crying, but then DD basically just got pissy, and said "I thought you were a good mommy, but now you are being a bad mommy!"
She stayed up there for about 15 minutes, then came down and was being cranky and annoying, clearly seeking attention, but refusing to apologize and showing no remorse. she eventually came out of it and started being nice, but said that she didn't feel bad about biting the baby."
This is not accountability. It is permissiveness. I do not have perfect kids and I know what it's like to be the parent of the biter -- I speak from the experience of having had two kids (my twins) who went through a bad biting phase (when they were 18 months old). My husband is a professor of child development at a major university and we have done our best to provide our kids with consequences that mimic what they will experience in the real world (as appropriate to their age, of course). When you do socially unacceptable things like bite, people are don't like it and don't want to be your friend. For a two year old this means using an angry mommy voice and removing the child from the play date for a period of time. For a four year old this means putting on a show of being absolutely horrified and certainly not allowing the child to rejoin the social occasion that day.
I think the princess thing is a bit of a stretch, fwiw.