The judge need not be prejudice if you know who to deal with the problems of false allegations. When you go to court, do you have people there as “Court Watchers?” They take notes on what is going on, and makes sure the judge knows they are. I have a court watch form that can be used. Also, what is your husband doing to curtail false allegations.
Does he keep a daily journal? When he picks up the children, does he take witnesses along, and especially someone with a video camera? Has he considered suing her for defamation of character? Juries are not quite so easy to put one over as a judge is. And don’t forget, a judge does go by the evidence. Did he present significant evidence to counter her claims?
There is a lot he can be doing to counter her. But, it takes the time to learn what he needs to be doing, and have the nerve to do it.