AITA for not picking up my half sister when she called me.

sorry for any errors, not a native English speaker

I (27M) have a half-sister (16F), the illegitimate daughter of my father and a former colleague of his. For the past two years, she and her mother have lived separately from us, and we’ve had no contact whatsoever. I only knew of her existence because my father sponsored her education. Of course, my mother never really liked this situation, but it became worse after my half sister’s mother passed away, and my half sister moved in with her.

My father went through a lot of trouble to gain custody of her, and eventually she moved in with him and my mother. My father is often away from home, so most of the time it’s just my mother and half sister at home, and their relationship isn’t good. A week ago, she (half sister) suddenly called me and asked me to pick her up. I asked her why she needed to come, since she was already home, and she said my mother told her to leave and she couldn’t go anywhere. I told her I wasn’t going to let her stay with me overnight and then hung up.

My dad called and yelled at me because she stayed overnight at a friend’s house, and the friend’s parents also called him, which embarrassed him. My girlfriend thinks I should have picked her up because she might have gotten into trouble, but I don’t feel it’s my responsibility; after all, it was my dad’s terrible decision to bring her to our house. Since she ended up staying overnight at her friend’s anyways, I don’t think I did anything wrong.

Edit: Ok, after reading through the comments, I considered again how I would feel if something had happened to her, or if she didn’t have a friend to take her in that night, and I feel guilty about how I handled it. I saw the drive as more of an inconvenience than helping her, and I did not want her in my home because of the pain that she represented for my mother. However, I should have tried to reason with my mother, or make my father deal with it directly instead of doing nothing.