was the mom actually the mother of the attic girl?

I believe she was the girl's biological Mother. At the point where the Dad is describing the girl's birth, he nods towards the Mother when he states how she was 'covered in the sh*t and p*ss and stink of her mother'. Mother acknowledges the comment was directed at her with a stiffenning of her back and a slight turning away of her head as if hurt but trying to retain her dignity.

I also believe that the girl in the attic was her biological daughter. You have to remember that the mother wanted a "Perfect Daughter" and the girl in the attic obviously wasn't high enough for her standard. The girl in the attic was handicapped and couldn't even eat her own food which disgraced the Mom. The Mom adopted Birdie (probably when Birdie was little) and shaped her into becoming the perfect daughter for her, she wanted Birdie to be everything her first daughter never was. You can also see it when Lena gets kidnapped how she tries to make her into a perfect daughter too.