My girlfriend has a brother and I am not going to meet him.
Why aren't you going to meet him?
He's a big gangster and I'm certain that him being around would cause me nothing but trouble.
It is okay to be scared to meet a partner's family but it will happen someday, you cannot avoid it forever. If you hope to continue the relationship you will be meeting all the people that she loves.
For the first time in my life, I'm pretty sure it is not going to happen.
Your girlfriend expects you to meet her brother, but if this is something you feel strongly about then you need to have a conversation with her and explain your reasoning. Meeting the family of partners is the norm and she will wonder why you won't meet him.