public class Person {
  private List<Dog> dogs;
  // getter and setter for dogs
}

public class Dog {
  private Person person;
  // getter and setter for person
}

public void removeDog(Dog dog) {
  dogs.remove(dog);
  dog.setPerson(null);
}

public void addDog(Dog dog) {
  dog.setPerson(this);
  dogs.add(dog);
}

Dog dog = dogDAO.getDogById(int id);
dogDAO.remove(dog);

Person person = personDAO.getPersonById(int id);
Dog dog = new Dog();
dog.setPerson(person);
dogDAO.save(dog);

dogDAO.remove(person.removeDog(dog))