My mom was married before my dad. Her first husband was abusive, mentally and physically. They had a daughter together and eventually my mom got the courage to leave him.
She met my dad and never really spoke to her first husband anymore. My older sister is not technically my dads daughter but she's always called him dad. She still visits her real dads mom, but has no real contact with her biological father.
My older sister has always been my sister and not my half sister.
I don't think Cory has done anything to warrant you or your childs attention.