amber - huge congratulations on the birth of your lovely daughter, sorry your family are causing all this hassle.
Names are an emotional issue, but your brother and Mum are being completely unreasonable and unkind. Your dd's name is special, and you should be ab;le to call her what you and her dad most wnat to call her.
No wonder your brother is so spoilt, selfish and bullying if your Mumsticks up for him and uses emotional balckmail like this. how dare she get tearful - and THEN tell you she doesn't like your second choice name.
Go forward cheerily, call her Emma, and maybe write a letter direct to your brother and SIL and say sorry they have reacted like this, you never imagined they would, but as Emma is a well-known enough name thsy haven't got copyright on it and of course it is no refelction on how you feel about any of them, and you have no doubt that the children are strong enough in their individulity to have strong identities, even if they have part of thier name oin common.
And that if he makes it a probelm, that is sad, but not your fault.
Otherwise, his bullying is now extending to your little girl! Why should he be alowed to say what she should or shouldn't be called??
Good luck.