Depending on the nature of your custody arrangement, it is likely that your children are required to split time between two houses. Things can get complicated when your child may not want to go to one house or another. This refusal can occur for a wide variety of reasons and it is important to understand the impetus for their objection as well as a few tools you can use to talk to your child to work through this issue.
Did a specific negative event occur?
Maybe your child got into an argument last time they spent time with their other parent. If your child has not expressed unhappiness about the visitation arrangement previously, it is very possible that a specific event or conflict is at the heart of this problem. Talk to your ex without accusing them of anything, explore the situation in a non-judgmental way.
Is there a disparity between the lifestyles of each parent?
If at one house your child has all of their favorite toys and snacks but at another house they are living a hotel-like existence, they may be objecting to the visitation out of a desire for continuity and not animosity toward the other parent. This is a more readily solvable problem that can be alleviated by creating a home like space at both homes. This may require the purchase of duplicate items that are of great import to your child.
Are you speaking adversely about the other parent?
This is a hard thing to admit to but if you are speaking negatively about the other parent or remarking negatively about their child care abilities it is very possible that your child is objecting solely out of a desire, conscious or not, to appease you. In a situation like this it is critical that you do not place the necessity of the visit on your custody arrangement but rather take this opportunity to explain to your child how much their other parent loves them and how their relationship with both parents is equally important.
If your child is frequently refusing to participate in the custody arrangement it is possible that it should be reevaluated in consultation with a family law attorney and a psychologist. If both parents are emotionally healthy and able to parent safely, the children should have time with each parent. Help your child work through this issue to help them reach their psychological potential.