I wanted to know whether I was bu to believe that I am not being unreasonable to be upset at how my mother talks about me in front of my dd and others.........
It was intemperate and conveyed contempt. She absolutely should not have done it.
You come across as a good mother, with the ability and determination to put your DD first. I understand your reluctance to start proceedings to get her back. A court order situation could go either way, though most likely against you, given the DD is with family and you are in the UK in accommodation that is only suitable for one.
My advice to you would be to maintain contact with DD as much as you possibly can, keep on demonstrating your love for her, and keep channels of communication open for her. I would encourage your siblings to keep in contact with her too if they are not already, even the brother who did not have your back.
This may be hard, but try not to bad mouth your mother when talking to DD. Don't give her the impression that she is caught in the middle of a struggle between you and your mother. There will be plenty of time to debrief DD and compare notes when she is able to make up her own mind about where she lives. Focus on keeping the contact frequent and positive for now.
Keep up the work on your journey to better mental health.
Try to anticipate problems like when presents might be opened, and figure out how you can avoid the need for communication with your mother. In the case of the presents, writing 'FOR CHRISTMAS' prominently on the package would have avoided the need for contact.
You most likely feel that somehow, some time, if you keep on trying, a stone will be rolled away, or the wind will part the waters, and your mother will have a change of heart. Maybe you hold onto the hope that one day you will receive what you need from your mother in terms of affirmation and decent treatment. It is incredibly hard to deal with being cast as the black sheep, being scapegoated, rejected, used as someone else's emotional punching bag. Have you ever had therapy to deal specifically with the effects of narcissistic parental abuse? Giving up the hope of love is incredibly wrenching, and involves grief even worse than that associated with death because while there is life we always want to hope.
Ginger1982, and others, the DD and the OP's mother are in Ireland, where social services prefer to keep extended family involved as much as possible in fostering arrangements. The OP most likely had absolutely no choice about where her DD ended up, and narcissists can bamboozle people very effectively into believing they are nice people.