Communicate to your child that the divorce was not his or her fault.
Even if your child says that they never thought that it was, it will be reassuring to hear that you don't think so. Get your own therapist so that you are not tempted to have your children fill that role.
Even if it means getting a job, taking a loan, or asking someone to help out financially until you can make necessary changes. Remember that all the changes and issues that are troubling you are probably troubling them, too.
If you make them feel that you are unable to handle it, they lose their sense of security.
Your child might be quiet and may not want to share any feelings. If you think that it might be related to a lack of emotional vocabulary, help your child develop one. A good therapist can help you to process what has happened in your marriage and afterwards. Respect that your loss is different from your child's.