is it normal not to accept my husband's child

Then why did you marry him? You knew of this other child. And it truly doesn't matter how you feel about the child complicating your children's lives, because its already done. That is their step-sister whether you like it or not. And to be so hateful to a child is awful. Perhaps for everyone's best interest you should reconsider this marriage. By not accepting his daughter, you are not accepting a vital part of him.

Imagine you die, or divorce and his next wife exclaims the same. She doesn't accept your children. She feels they are not her problem and doesn't want to raise them. Would you expect him to choose her over them? Of course not, it is insane to make a man choose between you and his own child!