My boyfriend has a biological child with his ex....?

My boyfriend of 9 months has a 5 month old daughter with his ex-girlfriend and I explained here before how they had broken up many times, this was an unplanned mistake, but she wanted to keep it anyway. I have accepted the baby and the mother has gotten a lot better (no more evil messages, phone calls, etc). BUT my issue is that this ex has a 10 year old daughter with a different man. My boyfriend got together with her when the child was 4 years old and then broke up when she was 9 yrs old. He still insists on having a relationship with the girl. Just because he is the father of her sister doesn' t make him the older child's father. Now when the baby comes over, the 10 year old visits with her. Am I being unreasonable by thinking this little girl is not my boyfriend's responsibility??? It was hard enough accepting the infant, I just can't get past the fact that he should not have responsibility for the older child. Is it terrible if only the baby comes over and not the 10 year old? To me it seems like the ex gets an automatic babysitter when both kids leave her house. Any advice negative or positive would be appreciated.