Child custody cases are difficult on everyone involved. The children have to adjust to a new way of life that they might not appreciate very much. There might be times when they are with you that they start to miss the other parent. This is perfectly normal but it can be a shock for you to have to deal with.
Oftentimes, these assertions that they want the other parent are going to come when the child is frustrated or overly tired. These situations can cause them to lash out and want what they know they can't have, especially when they are younger and can't express their emotions like an older child.
Even though it is hard to think about, you need to be sure you aren't making the situation worse by ignoring the child's pleas for their other parent or making them feel bad about their feelings. Work with your child to find out what you can do to make the situation easier. Maybe calling the other parent or using a video chat to speak to them will quell the desire.
Do your best not to get angry or upset. More than likely, your child isn't saying anything wrong with you as a parent. It is often just that they don't know how to cope with the major changes going on. As the time marches forward, they might become more accustomed to what is going on so they won't feel as stressed.
When your children are having issues like this, it is best to try to keep things consistent. Working out a child custody agreement quickly can give you the foundation to do this without having to worry about needing to change things up again too soon.