I'm going to refuse to play piano in front of my mother and her friends
Why don't you want to play piano for your mother and her friends?
She is going to use it as an excuse to have fun at my expense.
You have the freedom to do whatever you want and no one can force you to do anything.  If you don't like playing piano for your mother and her friends, you should tell her that and she respond with kindness and understanding.  If she really loves you, she will not be disappointed.
I'm 12 and I don't care.
Even at 12, you should have the freedom to make those choices. Have you talk to you mom about her using you?