How should I feel? Sibling just discovered. Plz help.?

My parents were on and off throughout my early childhood and after I turned 9 I had no contact with my father. I'm now 20. My father contacted me this year asking for another chance at being in my life(it wasn't really my decision that he wasn't in my life in the first place but my mom's- he abused her, used drugs, alcohol). We(my brother, sister and I) have talked a couple times and I found out that we have a half sister. She was born when I was 6 and I'm not sure if my parents were together but it seems like a touchy subject when I ask about the situation. I ume he cheated on mom. Anyway, when I found out about my half-sister I was happy and overjoyed that I have another sibling and curious to meet her. My brother and sister and mother however don't want anything to do with her and dont think I should either. I'm having a hard time understanding all this. Am I abnormal for feeling happy about it?