I recently read a horrific story from Pro Publica on exactly what you are describing here. The child is obviously being abused by the father, and yet the father gets full custody! He uses the "parental alienation" defense you mention here and convinces the people in power in his small town that mom is the "crazy bitch" character you describe. It's a truly heartbreaking story. I can't imagine what I'd do in that situation. Kidnap my own child and flee the country? There is no justice or safety the mother and child can obtain. Patriarchy is evil in all its forms. :( https://www.propublica.org/article/both-parents-agree-child-is-being-harmed-who-will-courts-believe