You got offered to be his bloodbag because of your family's sake. You're fine with it... As long as you can get away from that family of your. It's still two sided benefits. You get to leave this family and he can keep drinking your blood to control himself even though he act cold and disgust towards you and push you into living in secondary mansion. From what you know he's a vampire... more than 500 years at least. But so what? At least you can be free and do whatever you want there.