She asked if she could call me mom...

So I have a 9yr old little girl that was placed for adoption at birth. I found her aparents through the same agency that handled my adoption (I am also an adoptee). I met them when I was 7 months pregnant. Long story a tad bit shorter, aparents divorced when dd was 3 years old because adad was doing "bad" things to her. Amom didn't want to put dd through the hell of rape kits ect...and so adad signed his right away. she still for some messed up reason allows him to see her a few times a year (supervised). Fast forward to last may amom started dated and very quickly let her new bf move in. He tells me hes not really a "kid" person. I have done my best to be supportive of everything amom does because if I am not she doesnt let me see dd for along periods of time. Shes pretty neurotic. I have lots of issues with her but I would never tell her that. anyway so she has this new live in bf and all of a sudden I am allowed to take dd over night. Our first "sleepover" at my house lasted 7 days. she went home for 2 days and came back for another 8 days at my house. I am now able to have her all the time because she interfers with the new bfs relationship with amom. Fast forward to now So dd knows she is adopted she calls my 3 girls her sisters. I have had talks with her about my own experience being adopted and even my reunion with my own bmom. We have gotten very close over the last year. Well on saturday she was at my house for our weekend sleepover she was sitting on my lap being silly and stopped turned to me and asked if she could call me mom....I was so unbelievably shocked. I know she and her mom have issues and she has asked me many times if I could just take her back, but I always remind her that her mom loves her very much and would be very sad without her, and that I love her very much but would never take her from her mommy. (All very very hard topics btw) I told her that if she called me mom it would probably make her mother very sad and could hurt her feelings then she asked me if she could just call me mom while we were together without amom there. I told her yes. I have no idea if that was the right answer, I know she is just a little girl trying to get confirmation that she is special and she is loved, but I just dont know what I was supposed to say. I love DD so much I dont want to do anything to hurt or confuse her down the road. I could write a book that no one would ever believe about my open adoption with dd, too much to put in one post. I just need some support, and even more I need to know Im not alone. I havent been in adoption.com for many years. But I am starting to feel very alone in this again.