The children maybe reflecting the parent's feelings, not expressing their own. The children may believe it pleases the parent for them to be sad about leaving. The children may be telling the parent what they think the parent wants to hear. The children may simply find changing from one parent's home to the other uncomfortable. This is usually a temporary upset.
Some children welcome change.
Others have a more difficult time with it. Parents ought not jump to conclusions when a child resists visitation. Just as important as figuring out the children's true concerns is finding solutions to the problem. The first solution many parents propose is to stop visitation. That is almost never the best answer, and the counselor can also help the parents devise ways for the children to comfortably spend time in both homes.