Divorce is a messy battleground where children are the innocent victims. It is extremely important to keep the children out of the action. They will take the blame on personally for the breakup of the family and will feel that the arguments centre around them and their actions. Try to keep as much of the arguing / discussing away from the kids. Obviously they will sense and know that things are not right. But, they should not be in the centre of the problem.
To ease the pain of separation or divorce on children, both parents should ensure that their homes retain enough of the familiar things that the kids recognise as home. The child is looking for comfort in a time of great uncertainty. Give them a familiar environment to feel immediately comfortable in.
Divorce is hard for kids to cope with. Let them know that they are not to blame in any way. Allow them their space and time to deal with what has happened and listen to them. They have their view and their right to that view.