Is it normal, not to be allowed to see your parent's family?

When I was born, I had contact with both sides of my family, but when I was about 3 my father died. At some point my mother's family cut off contact with my father's family. The only person allowed to keep in "contact" was my aunt/godmother. I remember growing up and it was just my mother's family and no one else... At some point, I remember my aunt came over one night to give me a birthday present. My mother refused to let her in the house, but we talked for a little bit. My mother got the package and basically slammed the door in her face. She seemed angry at me for talking to her.

Over the next few years, my aunt would continue to send me birthday presents. The presents would often come late and my immediate family would often be filled with contempt ,especially when she asked if we could get in contact, but I was just too naive to see it.

Sometime last year, I got a letter from my father's grandmother. In it she wrote about my cousins and how she wanted to get in touch so she wrote down her number. It was around my birthday so she put $20-$50 in it. My family was acting very cruel and demanded to read it. They were very angry about the letter and the money. Saying that they were surprised that my father's family actually cared about me,etc. I was excited about talking to them, but I was also stupid. I told my mother and she became very angry at me. She forbid me to talk to them until I was in college. I demand to know why and she said she accused them of being "Racist and that they would compare me to the others". I've asked her many times since to tell me the truth, but she has "avoided" it.

I had my birthday on saturday and I got a card from my Aunt. In it she wished me a happy birthday, but stressed that she wanted to talk to me. She left her number, email and Facebook. This time most of my immediate family didn't read it and my mother has shown some indifference to it, but it has got me thinking about the whole situation....

It makes me feel bad. I feel like I'm hurting my father's family's feelings and getting their hopes up. I've never had the chance to properly voice my feelings toward them as my mother's family has always "censored" the content of my cards. I'm also growing angry at my immediate family for doing this all these years. Reading about my cousins makes me angry that my family has deprived me from getting to know them. If I was allowed to know them, maybe I wouldn't have so many problems now. Maybe, I wouldn't have been so lonely or had a better way to buffer the abuse I've had to deal with. I never gave much thought and at times didn't even know that they existed until now! I don't even know what they look like except for the photo album but those were from about 10-20 years ago! I'm upset and confused over this. I'm going to college next year and I really don't know what to do or expect. I guess my question is whether or not it's normal for a family to do such a thing to someone? Please, is this normal?