How can I get information on a specific child custody case?

My daughter is living with an abusive man because some how he was given custody of there daughter. She has moved out 3 times but the abuse is still there. He holds there child and tells her mommy doesn’t love her that’s why she lives some where else.Says things like mommy is a fat ***, She’s at the**** bar … She is so miserable she just needs out. What does she have to do to get out with the child?

She needs to call, or you do, child protective services. They are there for the child first, many women are kept afraid that if the authorities come looking they will judge both and take the child away from both. In fact, they may well threaten to take the child from him for being abusive, and from her only if she is ennabling and contributing by remaining.
The courts want the child with the better parent. If he is seriously abusive she should call 911, get a restraining order and have him removed. An interim order, possibly for supervised visitation rights but not permanent, could be placed pending any criminal charges. Though it is better to remove herself and the child to where he cannot find them.