Ok, quickly putting my .02 in and I mean this post kindly. I have four adopted kids. All of them, even my Autism Spectrum Disorders (ASD) son, thinks of himself as having two mothers, although they are careful to be easy child around me. I am Mom who takes care of them. But there is this mystery woman who looks like them and maybe is more like they are (good or bad) and that they do think about and she also is called "mother" when the child isn't talking to me. Sometimes I even hear "real mom." They don't mean they don't love us or don't think of us as THE Mom. It means "she gave birth to me." I used to feel hurt, but talking to my older kids, I put it in perspective. Also, I have a best friend who found her birthmom at age 37. She calls her "Mom" to her face, but she is "Sue" (not her real name) in private. To me, she says her adoptive mom is really her mom--and her adoptive mom was no prize, an alcoholic. Her birthmom is actually really cool and enfolded her into the family right away--but the more she knows them the more she sees that they are dysfunctional too. It did help her a lot to see who she looked like, why she is musically gifted, and she liked meeting her siblings. It is natural for adopted kids to think different then us, their parents. They always have this "who are they?" in their minds.
So far none of my kids have searched, although they can and we'd help. I think they may once we're gone, and that's ok. I don't mind being one of the moms--the one who did the hard work! But if my kids refer to birthmom as mom too, well, I'm not going to let it bother me because I think it means "you who gave birth to me and whose genes I shared." Although my son we adopted at age six is not close to us, or anyone in the family, I know my once drug-addicted daughter loves me very much, and I her. I doubt she could form any closer a bond to anyone else because we've been through hell and back together and, in the process, have come full circle and have a very strong, unbreakable relationship. I am confident that no birthmom can take my place, even if she finds her and calls her "Mom." I don't believe your daughter meant YOU aren't her mom--really. And I"m sorry it hurts because I've been there. JMO