If one parent leaves out of town and leaves the kids with a relative can they keep the kids from the father?
This would be applied if the father has a restriction order, placed on him to stay away from them. If the father has a bad record, the relatives may also decide to keep the kids away from him in future. You may consult a lawyer to clear this up.
not unless the father has a court order telling him to stay away or he has given up his parental rights in court.