So I have been down this road. My Mom doesn't like DS's first name much. So she decided to call him by a nickname off his middle name.
His name is Kevin Patrick. She calls him Paddy. I just let her do it even though it bugs me a bit. At first my inlaws and husband were the ones who had a major issue with it. But they thought she was calling him Patty as in a girls name.
I figured she would either eventually concede or I would just get used to it. Most of the time it is a little of both. Sometimes she calls him Kevin but most of the time she calls him Paddy.
It doesn't seem to bother him much, although he rarely will acknowledge her if she calls him Paddy. :-) At Christmas she did want to get him a personalized stocking. I told her that if it was for our house it had to have his first name, the one at her house could have the nickname.
It did also help us though that we didn't pick a name until after he was born.
I hope this helps you some. I do agree that it is crazy for your mom to just pick a name. At least ours is a version of his name. As to her saying that she is sad with the name you chose. My response would be- "You raised me, raised me well, and this is my child. My husband and I have the right to name our child what we want. We respectively ask that you honor our wishes. She is our child, not yours.
Good luck!