I agree that this is soooo not about generosity. It is about what is best for the child. I was really comfortable with my daughter calling her birthmother 'mommy firstname." But many social workers counseled us against it and it was written into our open adoption agreement (without our knowledge) that the birthmorther was never to refer to herself as mother. Looking back, I am so glad I took the advice. It was just the first of many times I had to put my foot down and be my daughter's advocate in her relationship with her birthmother.
I think in your DD's situation (with her attachment, and other, issues,) it's a good thing. But in my kids cases, they don't have the negative effects of their early lives. Neither of my kids uses the "Mommy/Daddy" labels with their birth parents but it wouldn't matter to me. I am their mother but I'm not the only one they ever had. DS's bio-grandmother is "Grandma" to both of my kids. It doesn't lessen the relationships they have with my parents and step-parents.When DS's birth mother calls and wants to talk to "her son" it catches me off guard but I know what she means. He'll always be her son. Our son.