First, Check out your states grandparents rights laws, yes grandparents do have rights, they are usually unaware of them because they do not ask the proper authorities or the right questions. This could help you get visitation as well as give you time to see how the child really behaves when he gets used to you.
Second, definitely call childrens services so they can investigate the home and the father. If this man has a history of violence you should also begin to gather your evidence- times dates police reports restraining orders etc. whatever kind of paper trail you have to document his abuse reflects on his character and his suitabliity as a parent.
Third, your daughter must try to establish more contact with her child, does he attend preschool? she should visit or volunteer as a room mother an hour a week or something. Is he in any childrens classes - kindermusic or gymboree for example? she should accompany him to these classes. She has to get involved in his life. Call him and talk on the phone for a few minutes each day. She has to prove that she is determined to be a part of his life to reestablish the relationship and her rights as the noncustodial parent.This means she must have all her ducks in a row regarding her parenting ability, housing, child care, and her surroundings and activities. She has to basically present her self as an involved, caring, loving parent if thats what she wants to be.
Finally, talk to the officer at juvenile court - or whoever assigned custody and see what recourse she has to appeal her decision, based on her suspicion of abuse, and the fact that he lied.
Do not give up, the stake of this childs life and future is not something to take lightly.