If a woman in a situation of domestic abuse flees, does she weaken her claim on custody of the children?

Sometimes domestic situations deteriorate to the point where a woman does not leave the home; she escapes it without her husband knowing where they went. After a divorce, her husband may claim she stole the children and that she did it just to get back at him. In a custody case that reaches this level, a woman can enter evidence of domestic violence, such as a Temporary Restraining Order, police records, or court records. They can be used to show that she removed the children for her and their safety.