Anger is a natural part of coping with any loss. In this case, the child has lost several things that he or she needs to grieve over. First, there is the loss of the security of the home. The uncertainty of the situation coupled with the feeling that the child may in some way be responsible can be overwhelming for a young mind.
There is a sense of loss when one of he child's parents no longer is in the picture except for every other weekend and some holidays. Even a parent who is not overly attentive to the child is usually around more than that when the family is still together. Some children feel that they have lost their identity. Their place in the family has now shifted. This uncomfortable shift can easily lead to anger.
When discussing how to deal with an angry child following a divorce, these factors need to be examined to find what is disturbing your child the most. The age of the child can play a big role also. Extremely young children mostly need help to face their inability to understand what has happened.
The parents have to find a way to compensate for the fact that mom or dad are no longer in the house. The shift from place to place is a factor here. So, also is the reality that the child may no longer live in the family home depending on who got the house or if the house survived the divorce.
For children between four and 10 or so, time must be allowed to pass for the child to process what has taken place. If this is rushed, the anger can move from part of a process to a major dilemma. Try to find ways to restore things to as close to normal as possible.
Keep up daily routines. Do not indulge the child or become too permissive. These children need to see that the structure of the home is being restored. It may not be quite the same, but it is still a safe place to be.
For older children and teens, avoid lumping excessive responsibility on their shoulders. Teaching them to help is not the same as expecting them to suddenly take over as the second parent in the house. At 13 to 17 years old, they are not really adults even if they are starting to look like one. Be careful to explain the what and why behind any new responsibilities and expectations. Anger at this age can become rebellion. It is better to ask too little than too much. Again, try to avoid the other extreme of becoming overly permissive.
Regardless of age, resist trying to just throw money at the problem. Your children need you not more things. This unfortunately comes at a time when you are being crunched for time and money as you try to get your own life back on track. If it is possible during this time, one of the best solutions to the anger problem is for the parents to work hard to iron out their differences and not work against each other. It is hard to fix something that the other parent keeps making worse.
Anyway, that's just something from my own experience.