My son & his girlfriend broke up. She wants full custody of the dog. What type of lawyer would he need need?

Animal custody cases can be brought in District, City, Village or Supreme Courts. If your son's ex girlfriend sues for custody, there will be a hearing, and the judge will hear evidence and testimony and the decision will be made based on the best interests of everyone involved. The court takes into account who spends the most time with the dog, who's paid vet bills, who has a place that's most comfortable for the dog, etc.  Sometimes the court awards joint custody, depending on the facts of the case.