Divorce can kick off a number of disorders - Separation Anxiety Disorder is one of them. The signs and symptoms include fears that someone is going to kidnap a child or their parents, inability to stay in bed, intrusive nightmares, and difficulty settling down for sleep. Sometimes it can be so powerful that a child will refuse to go to school, they will get stomach aches that will prevent them from going to school, or they will force the school nurse to send them home.
This disorder usually runs in the family. Take a look to see if you or your spouse has any anxiety disorders running in your family backgrounds. Divorce is a breaking of trust for most children. They expected a family to continue forever and when it breaks some kids feel like the bottom has fallen out.
So don't be surprised if there's an increase in separation anxiety soon after mom or dad moves out. There is treatment for this issue and it includes supportive psychotherapy, reassurance, and occasionally, but not necessarily, medication. If a child is refusing to go to school, you have a serious problem on your hands that needs intervention. It's like falling off a horse - they longer you're off that horse or out of school the harder it is to get back into the swing of things.
In my experience, separation anxiety disorder is quite treatable, but it is something that parents often let go for too long. After a divorce, get help and take your own pulse as well - you don't need any extra anxiety during this time. Don't be too worried because your child should get better with a little bit of time and treatment.